The density profile of a Coulomb plasma on a cylinder: boundary oscillations

Alexander G. Abanov; Gabriel Cardoso; Jean-Marie St\'ephan

REVIEW 4 major objections 4 minor 46 references

The density profile of a Coulomb plasma on a cylinder: boundary oscillations

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read On a cylinder, the boundary density oscillations of the 2D one-component plasma have a wavelength that locks to the triangular lattice-plane spacing $d_0 \approx 0.93$ as $\Gamma$ approaches the freezing transition, while the damping…

desk verdict Worth refereeing: a genuinely cleaner cylinder setup and a new oriented correlation function, but the fitted claims need error bars and a test of the commensurate radius. read the letter →

arxiv 2412.15345 v1 pith:E37OADB7 submitted 2024-12-19 cond-mat.stat-mech cond-mat.str-el

Gabriel Cardoso , Jean-Marie Stéphan , Alexander G. Abanov This is my paper · ORCID

classification cond-mat.stat-mechcond-mat.str-el MSC 82B2182B2682B80

keywords two-dimensionalone-componentplasmaboundarydensityoscillationscylindricalgeometrytriangularlatticefreezingtransitionphase-fieldcrystalorientedcorrelationfunctiontopologicaldefects

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper uses Monte Carlo simulations of a two-dimensional one-component plasma wrapped on a cylinder to establish a sharp picture of boundary density oscillations in the strongly coupled fluid. It argues that, as the inverse temperature $\Gamma$ approaches the freezing transition $\Gamma_m \approx 140$, the wavelength $\lambda$ of the ripples near the boundary converges rapidly to $d_0 \approx 0.93$, the spacing between triangular lattice planes, while the damping length $\xi$ increases sharply. Because the cylinder circumference is chosen to fit an integer number of lattice spacings, the geometry removes frustration and disclinations, so these oscillations can be attributed to freezing at the edge rather than to geometric artifacts. The paper also proposes an oriented correlation function $g_x(x)$, defined by aligning each snapshot with the particle closest to the test particle, which matches the boundary-density wavelength much better than the radial $g(r)$. This connects boundary profiles to bulk correlations and to the melting transition through a phase-field crystal description.

What carries the argument

The load-bearing object is the unfrustrated triangular lattice on the cylinder, obtained by fixing $R = m a_0/(2\pi)$ so that $m$ spacings $a_0$ fit around the circumference; the lattice-plane spacing $d_0 = \sqrt{3}a_0/2 \approx 0.93$ is the wavelength that boundary density oscillations converge to. The oscillations are quantified by fitting $\rho(x)$ to $e^{-x/\xi}\sin(2\pi x/\lambda)$, producing the damping length $\xi$ and wavelength $\lambda$. The phase-field crystal free energy $F[\psi] = \int d^2x\,( \frac{a}{2}\psi^2 + \frac{b}{2}\psi(\Delta + q_0^2)^2\psi + \frac{u}{4}\psi^4 + V\psi )$, with parameters linked to the bulk direct correlation function through the Ornstein-Zernike relation, connects the boundary profile to the static structure factor peak. The paper's new instrument is the oriented correlation function $g_x(x)$, defined by rotating each snapshot so the particle closest to a test particle lies along the $y$-axis; the density along $x$ then tracks the boundary profile more faithfully than $g(r)$. Together these objects carry the argument that edge oscillations are freezing signatures and that an anisotropic PFC action is needed.

What would settle it

Run the same Monte Carlo simulations on cylinders with incommensurate radii, for example a value midway between two consecutive commensurate values, at $\Gamma = 130$; if the fitted wavelength $\lambda$ shifts away from $d_0 \approx 0.93$ or the dislocation density changes sharply, then the commensurate choice is pinning the observed boundary physics rather than revealing a thermodynamic property.

Watch

Extended reading notes

Core claim

The central claim is that damped oscillations in the boundary density profile of the two-dimensional one-component plasma on a cylinder are a thermodynamic signature of a crystalline layer freezing at the edge. With the radius fixed to $R = m a_0/(2\pi)$, exactly $m$ triangular-lattice spacings $a_0$ fit around the circumference, so a perfect triangular lattice can form without disclinations; the lattice-plane spacing $d_0 = \sqrt{3} a_0/2 \approx 0.93$ sets the oscillation wavelength. Fitting $\rho(x)$ to $e^{-x/\xi}\sin(2\pi x/\lambda)$, the paper finds $\lambda$ converging to $d_0$ as $\Gamma \to \Gamma_m$ and $\xi$ increasing sharply, consistent with a diverging correlation length at freezing. Comparing soft-wall, hard-wall, and mixed boundary conditions shows the profile shape is universal once shifted to the classical boundary, and the droplet squeezing shift is $\delta = d_0/2$. In the crystal phase, Delaunay triangulation shows the dislocation density $z$ is exponentially suppressed for $\Gamma > \Gamma_m$, with no strong divergence near the transition. Finally, the paper defines an oriented correlation function $g_x(x)$ whose oscillation wavelength agrees with the boundary-density wavelength far better than the radial $g(r)$, pointing to an anisotropic generalization of the phase-field crystal model.

Load-bearing premise

The load-bearing premise is that choosing the cylinder radius as $R = m a_0/(2\pi)$, so the circumference holds exactly $m$ lattice spacings, does not bias the physics; if this commensuration is what pins the wavelength to $d_0$ or suppresses defects, the universal-profile and exponential-defect-suppression claims would not survive for generic radii.

Editorial extensions

If this is right

The wavelength of boundary density oscillations in the strong-coupling fluid is set by the triangular lattice-plane spacing $d_0 \approx 0.93$ and is essentially independent of $\Gamma$, so measuring edge ripples gives the lattice constant of the incipient crystal.
The damping length $\xi$ increases sharply as $\Gamma$ approaches $\Gamma_m$, consistent with a correlation length that diverges at freezing; the cylinder geometry makes this trend cleaner than in disk geometry.
The density-profile shape is universal across soft-wall, hard-wall, and mixed boundary conditions once shifted to the classical boundary, and the squeezing shift $\delta = d_0/2$ follows from the lattice mismatch.
The dislocation density is exponentially suppressed for $\Gamma > \Gamma_m$, and the absence of a strong divergence near the transition is read as support for a weakly first-order melting picture, with the caveat that defect-divergence signatures can be numerically elusive.
The oriented correlation function $g_x(x)$ reproduces the boundary oscillation wavelength much better than $g(r)$, indicating that an anisotropic generalization of the phase-field crystal model would improve the calculation of density profiles.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: if the commensurate-radius setup is not generic, then incommensurate cylinder radii $R \neq m a_0/(2\pi)$ should introduce phase slips or extra disclinations; repeating the simulation at such radii would show whether the clean $\lambda \to d_0$ convergence and the exponential defect suppression survive.
Editorial inference: the oriented correlation function suggests a quantitative test for anisotropic phase-field crystal models, where direction-dependent $q_0$ parameters could be fitted to the same data and checked against the residual five-to-twenty percent discrepancies in $q_0$ and $a/b$ reported for the isotropic model.
Editorial inference: because the cylinder suppresses disclinations by construction, the exponential defect suppression above $\Gamma_m$ does not by itself discriminate between weakly first-order melting and BKTHNY; measuring the hexatic order parameter or defect correlation length in the same geometry would sharpen that distinction.
Editorial inference: the droplet squeezing shift $\delta = d_0/2$ derived from lattice mismatch on the cylinder could be searched for in disk-geometry profiles as a boundary-dependent offset, providing a quantitative bridge between the two geometries.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a solid numerical paper with a real new idea—the oriented correlation function gx—and a cleaner geometry for the 2D OCP edge. The central picture, that boundary density oscillations have wavelength approaching the triangular spacing d0 and damping length growing near freezing, is almost certainly correct. The weak spots are quantitative: fits without error bars, an asserted exponential law that never gets fitted, and an untested commensurate radius that could bias the universality claim.

What's new: the cylinder with the frustration-free radius R = m a0/(2π), mixed boundary conditions that let you separate normal and parallel fluctuations, and the oriented correlation function that aligns snapshots to the nearest particle. The droplet-squeezing shift δ = d0/2 in Eq. (13) is a neat parameter-free geometric identity. The defect-density curves from Delaunay triangulation are a useful complement to the density data.

What's done well: the paper compares soft, hard, and mixed boundary conditions, and disk versus cylinder, and shows that the density profiles largely collapse. The thermalization discussion is honest. The PFC treatment is used as a fitting framework, not over-sold as a derivation. The text is careful to mark numerical results as numerical.

Soft spots, in order: (1) No error bars or fit uncertainties anywhere. For a paper whose headline claims are quantitative, this is a real gap. (2) The exponential suppression of topological defects is stated without showing a fit; a slope and range would make it a claim rather than an impression. (3) The commensurate radius is a legitimate confound. At large Γ the ground state is an unstrained triangular lattice by construction, so the absence of free disclinations is partially built in. An incommensurate-radius simulation, even at one Γ, would settle whether the defect suppression and the λ→d0 convergence are generic. I don't think this is fatal—local packing near a wall should still prefer d0 spacing—but the paper should test it. (4) The conclusion favoring weak first-order melting from the absence of a defect divergence is, as the authors admit, numerically elusive. That claim should be soft-pedaled.

Who it's for: people working on 2D Coulomb systems, FQHE edge structure, and phase-field crystal models. It deserves a serious referee. My recommendation: send to review, ask for error bars, data release, and at least one incommensurate radius run.

Referee Report

4 major / 4 minor

Summary. The paper reports Monte Carlo simulations of the two-dimensional one-component plasma (2D OCP) on a cylinder, focusing on the boundary density profile, its temperature dependence, and its relation to bulk correlations. The authors find damped oscillations in the density profile whose wavelength approaches the triangular-lattice row spacing d0 as the inverse temperature Γ approaches the melting value Γm ≈ 140, while the damping length increases sharply. They argue that the cylindrical geometry removes geometric frustration and that boundary conditions do not affect the universal shape of the profile. They also quantify topological defects via Delaunay triangulation, report exponential suppression of dislocations in the crystalline phase, and propose an oriented correlation function gx(x) that better matches the boundary density oscillations than the radial g(r). The results are interpreted through a phase-field crystal (PFC) model with a single-peak approximation for the liquid structure factor.

Significance. If the main quantitative claims hold, the paper provides a useful step toward connecting boundary density oscillations of the 2D OCP with the crystallization transition and with anisotropic generalizations of PFC models. The cylindrical geometry is a natural setup for separating boundary-parallel and boundary-normal fluctuations, and the parameter-free droplet-squeezing identity in Eq. (13) is a clean analytic result. The paper also contains an interesting proposal for an oriented correlation function that may be more relevant than the radial distribution for wall-bounded plasmas. However, the central quantitative statements rely on fits without reported uncertainties and on simulations performed at a single, specially commensurate cylinder radius; these limitations currently prevent the claims from being fully established.

major comments (4)

[Section 4, Fig. 4] The wavelength λ and damping length ξ extracted from density profiles are presented without any error bars, fit ranges, or statistical uncertainties. Given that the claimed differences between disk and cylinder data are of order a few percent in λ and that ξ varies by about a factor of four over the plotted Γ range, the absence of uncertainties makes the statements 'rapidly converges' and 'sharper increase' impossible to assess quantitatively. Please provide error bars, the fitting procedure, the number of independent runs, and the systematic uncertainty associated with the choice of fit window.
[Section 2.1, Eq. (10)] All cylinder simulations use R = m a0/(2π), a circumference that is exactly commensurate with m triangular-lattice spacings. At low temperature the crystalline ground state then has row spacing d0 by construction, so the wavelength of boundary density oscillations and the suppression of disclinations are geometrically favored by the simulation box. The paper claims these features are generic for a cylinder (Section 4.1 and Discussion), but it never tests an incommensurate radius or varies m at fixed Γ. A test with incommensurate R, or at least a quantitative argument for why Eq. (10) does not pin λ and defect densities, is needed to support the universality claim.
[Section 5, Fig. 7] The claim that dislocation density is exponentially suppressed for Γ > Γm is supported only by an inset without error bars, a functional fit, or finite-size analysis. The text also states that no strong divergence is observed near the transition, but no statistical power or system-size scaling is given. Please quantify z(Γ) with fits and uncertainties, and discuss how the commensurate boundary could affect the nucleation of defects.
[Section 6, Figs. 9 and 10] The oriented correlation function gx(x) is described only verbally and in a figure caption; no defining equation is given. The agreement between its oscillation wavelength and that of the boundary density profile is assessed visually, without quantitative values or uncertainties. Since the proposed anisotropic PFC generalization is a stated motivation, a quantitative comparison of the wavelengths extracted from gx(x), g(r), and ρ(x) is necessary to support the claim of 'much more closely' matching.

minor comments (4)

[Section 4, Fig. 4] The left panel axis label 'Γh0' appears to be a typo and should likely be simply Γ.
[Section 6, Eq. (20)] The sentence comparing 'a0 ≈ 1.07 and d0 ≈ 0.93' in the q0 fit is confusing: a0 is the triangular lattice spacing and d0 the row spacing, and it is unclear which reference value 2π/q0 is being compared to. Please clarify.
[Section 2, Eq. (7)] The sentence 'ρ(x) = ρ(x) represents a one-dimensional density profile' contains a typo; it should state that the density depends only on the coordinate x under symmetric boundary conditions.
[General] No data or code availability statement is included; given that the central results are numerical, making the simulation data and analysis scripts available would substantially improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the cylinder simulation results are direct Monte Carlo measurements, and Eq. (13) is a parameter-free geometric identity.

full rationale

The paper's central quantitative claims are direct Monte Carlo measurements rather than derived predictions. The wavelength λ and damping length ξ in Fig. 4 are extracted by fitting the simulated density profiles, and the comparison value d0 ≈ 0.93 is fixed independently by the bulk density through a0 = (4/3)^{1/4} and d0 = √3 a0/2. The commensuration choice R = m a0/(2π) in Eq. (10) removes geometric frustration, but it does not by itself enforce the x-direction oscillation wavelength in the fluid; the near-agreement of λ with d0 is an empirical result, supported also by the disk data in Fig. 4. Equation (13), giving the droplet squeezing δ = d0/2, is a parameter-free geometric identity using only Eqs. (10) and (11). The PFC parameters q0 and a/b are fitted separately from ρ(x) and h0(r), and their 5–20% discrepancy indicates a genuine consistency test rather than a forced equality. The oriented correlation function gx(x) is defined from snapshots and compared to the density profile empirically. The only self-citation, Ref. [40] for the 'freezing at the edge' interpretation, frames the results but is not load-bearing for the new simulation data, which stand on their own. No step in the paper reduces by definition or by self-citation to its own inputs.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claims rest on fitted parameters (lambda, xi, q0, a/b), standard plasma screening assumptions, the authors' prior 'freezing at the edge' interpretation, the PFC single-peak approximation, and a commensurate-radius geometry that is not tested for generality.

free parameters (5)

Oscillation wavelength lambda = About 0.93 to 1.1 depending on Gamma (Fig. 4)
Fitted to boundary density profiles via Eq. (12); used to claim convergence to the lattice plane spacing d0 near Gamma_m.
Damping length xi = About 1 to 4, increasing with Gamma (Fig. 4)
Fitted in the same damped-sine fit; used to claim divergence near the freezing transition.
PFC wavevector q0 = Not tabulated; 2 pi / q0 differs from the density-profile fit by about 5 percent (Fig. 9)
Fitted independently to h0(r) and to rho(x); the comparison is between two fits, not an independent prediction.
PFC curvature ratio a/b = Roughly 100 to 400, differing by about 20 percent between fits (Fig. 9)
Fitted to h0(r) and rho(x); the residual discrepancy motivates the oriented-correlation proposal.
PFC coefficients a, b, u = Not determined in this paper
Appear in Eq. (15) as phenomenological parameters; the paper extracts only q0 and a/b, leaving the PFC model underdetermined.

assumptions (6)

standard math The cylinder Coulomb potential in Eq. (4) is the Green's function of the Laplace-Beltrami operator
Eq. (4) defines the interaction model; this is standard electrostatics on a cylinder.
domain assumption Bulk density is fixed to rho0 by charge screening
Eq. (8) in Section 2; standard OCP screening is used to identify the droplet boundary.
domain assumption Boundary oscillations are the melting signature of a crystalline boundary layer
Imported from the authors' previous work [40] and used throughout Section 4 to map the wavelength to d0 and the damping length to lattice displacement correlations.
ad hoc to paper The PFC single-peak approximation h0(k) = -1 + 1 / [a + b(q0^2 - k^2)^2] captures bulk correlations
Eq. (20); the parameters are fitted rather than derived, and the 20 percent mismatch motivates the proposed anisotropic extension.
domain assumption Delaunay triangulation coordination numbers identify topological defects
Section 5 assumes CN = 6 is a perfect lattice and CN = 5 or 7 are defects; no validation against other defect definitions is given.
ad hoc to paper The commensurate cylinder radius R = m a0 / (2 pi) is representative of general cylindrical geometry
Eq. (10); the paper never tests incommensurate radii, yet uses this setup to claim frustration-free generic behavior.

how reviews work

0 comments

Cite this review

Pith. "Pith review of The density profile of a Coulomb plasma on a cylinder: boundary oscillations." pith.science (2026). https://pith.science/paper/E37OADB7

@misc{pith2026241215345,
  author       = {Pith},
  title        = {Pith review of: The density profile of a Coulomb plasma on a cylinder: boundary oscillations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E37OADB7}},
  note         = {Machine review of arXiv:2412.15345}
}

read the original abstract

We present Monte Carlo simulations of the two-dimensional one-component plasma (2D OCP) confined to a cylindrical geometry, focusing on density profiles, fluctuations, and their connection to bulk correlation functions. The cylindrical geometry eliminates geometric frustration, allowing for a precise study of boundary density oscillations, the dependence on boundary conditions, and their relationship to the melting transition and triangular lattice structure. By triangulating particle configurations, we quantify the exponential suppression of topological defects in the crystalline phase. Furthermore, we propose an oriented correlation function that better links boundary density profiles with bulk correlation functions, motivating anisotropic generalizations of the phase-field crystal (PFC) model. These results provide new insights into the interplay between boundary effects, bulk correlations, and phase transitions in the 2D OCP.

Figures

Figures reproduced from arXiv: 2412.15345 by the authors.

**Figure 2.** Triangular lattice and particle position fluctuations. Left: A total of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Dependence of the density profile on temperature in the strong coupling [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Temperature dependence of the wavelength [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Comparison of density profiles with different boundary conditions at [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Two-dimensional density in the fluid phase. Left: A total of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: At high Γ, the particles form a triangular lattice with a few disclination defects (example shown on the left for Γ = 150, N = 1764), while at lower Γ, the density z of defects increases rapidly (example shown on the right for Γ = 130, N = 1764). The most common defect…

**Figure 8.** Figure 8: Radial distribution function g(r) for different values of Γ and N. The peaks of g(r) indicate short-range ordering in the system, becoming more pronounced as Γ increases, reflecting stronger correlations at lower temperatures [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: Fit of PFC parameters determined from the total correlation function [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]

**Figure 10.** Figure 10: Left: Snapshots with fixed particles (red). The density of particles around [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

46 extracted references · 39 canonical work pages

[1]

Statistical Mechanics of Simple Coulomb Systems.Physics Reports- Review Section Of Physics Letters, 59(1):1–94, 1980

M Baus and J P Hansen. Statistical Mechanics of Simple Coulomb Systems.Physics Reports- Review Section Of Physics Letters, 59(1):1–94, 1980

work page 1980
[2]

A monte carlo study of the classical two- dimensional one-component plasma

JM Caillol, D Levesque, JJ Weis, and JP Hansen. A monte carlo study of the classical two- dimensional one-component plasma. Journal of Statistical Physics, 28(2):325–349, 1982

work page 1982
[3]

de Leeuw and J.W

S.W. de Leeuw and J.W. Perram. Statistical mechanics of two-dimensional coulomb systems: Ii. the two-dimensional one-component plasma. Physica A: Statistical Mechanics and its Applications, 113(3):546 – 558, 1982

work page 1982
[4]

Anomalous quantum hall effect: an incompressible quantum fluid with fractionally charged excitations

Robert B Laughlin. Anomalous quantum hall effect: an incompressible quantum fluid with fractionally charged excitations. Physical Review Letters, 50(18):1395, 1983

work page 1983
[5]

Quantum Hall edges beyond the plasma analogy

Per Moosavi, Blagoje Oblak, Bastien Lapierre, Benoit Estienne, and Jean-Marie Stéphan. Quantum hall edges beyond the plasma analogy.arXiv preprint arXiv:2407.19013, 2024

work page Pith review arXiv 2024
[6]

W-infinity symmetry in the quantum hall effect beyond the edge

Andrea Cappelli and Lorenzo Maffi. W-infinity symmetry in the quantum hall effect beyond the edge. Journal of High Energy Physics, 2021(5):1–39, 2021

work page 2021
[7]

Hydrodynamics of euler incompressible fluid and the fractional quantum hall effect

PB Wiegmann. Hydrodynamics of euler incompressible fluid and the fractional quantum hall effect. Physical Review B, 88(24):241305, 2013

work page 2013
[8]

Statistical ensembles of complex, quaternion, and real matrices

Jean Ginibre. Statistical ensembles of complex, quaternion, and real matrices. Journal of Mathematical Physics, 6(3):440–449, 1965

1965

Show all 46 references

[9]

Log-gases and random matrices (LMS-34)

Peter J Forrester. Log-gases and random matrices (LMS-34). Princeton University Press, 2010

2010
[10]

Dualities for characteristic polynomial averages of complex symmetric and self dual non-hermitian random matrices.arXiv preprint arXiv:2411.07356, 2024

Peter J Forrester. Dualities for characteristic polynomial averages of complex symmetric and self dual non-hermitian random matrices.arXiv preprint arXiv:2411.07356, 2024

2024 arXiv
[11]

Complex symmetric, self-dual, and ginibre random matrices: Analytical results for three classes of bulk and edge statistics

Gernot Akemann, Noah Aygün, Mario Kieburg, and Patricia Päßler. Complex symmetric, self-dual, and ginibre random matrices: Analytical results for three classes of bulk and edge statistics. arXiv preprint arXiv:2410.21032, 2024

arXiv
[12]

Analogies between random matrix ensembles and the one-component plasma in two-dimensions

Peter J Forrester. Analogies between random matrix ensembles and the one-component plasma in two-dimensions. Nuclear Physics B, 904:253–281, 2016

2016
[13]

Lectures on coulomb and riesz gases.arXiv preprint arXiv:2407.21194, 2024

Sylvia Serfaty. Lectures on coulomb and riesz gases.arXiv preprint arXiv:2407.21194, 2024

2024 arXiv
[14]

The planar low temperature coulomb gas: separation and equidistribution

Yacin Ameur and José Luis Romero. The planar low temperature coulomb gas: separation and equidistribution. Rev. Mat. Iberoam, 39(2):611–648, 2023

2023
[15]

On the classical two-dimensional one-component coulomb plasma

A Alastuey and B Jancovici. On the classical two-dimensional one-component coulomb plasma. Journal de Physique, 42(1):1–12, 1981

1981
[16]

Cooperative phenomena below melting of the one-component two-dimensional plasma

Ph Choquard and J Clerouin. Cooperative phenomena below melting of the one-component two-dimensional plasma. Physical review letters, 50(26):2086, 1983

1983
[17]

On vortex lattices.Sov

V K Tkachenko. On vortex lattices.Sov. Phys. JETP, 22:1282–1286, 1966

1966
[18]

Destruction of long range order in one-dimensional and two-dimensional systems having a continuous symmetry group

VL Berezinsky. Destruction of long range order in one-dimensional and two-dimensional systems having a continuous symmetry group. i. classical systems.Zh. Eksp. Teor. Fiz., 32:493–500, 1970

1970
[19]

Ordering, metastability and phase transitions in two-dimensional systems

John Michael Kosterlitz and David James Thouless. Ordering, metastability and phase transitions in two-dimensional systems. Journal of Physics C: Solid State Physics , 6(7):1181, 1973

1973
[20]

Theoryoftwo-dimensionalmelting

BIHalperinandDavidRNelson. Theoryoftwo-dimensionalmelting. Physical Review Letters, 41(2):121, 1978

1978
[21]

Gauge Fields in Condensed Matter: Vol

Hagen Kleinert. Gauge Fields in Condensed Matter: Vol. 1: Superflow and Vortex Lines (Disorder Fields, Phase Transitions) Vol. 2: Stresses and Defects (Differential Geometry, Crystal Melting). World Scientific, 1989

1989
[22]

Note: Melting criterion for soft particle systems in two dimensions.The Journal of Chemical Physics, 148(14):146101, 2018

Sergey Khrapak. Note: Melting criterion for soft particle systems in two dimensions.The Journal of Chemical Physics, 148(14):146101, 2018

2018
[23]

Two-dimensional melting: From liquid-hexatic coexistence to continuous transitions.Physical review letters, 114(3):035702, 2015

Sebastian C Kapfer and Werner Krauth. Two-dimensional melting: From liquid-hexatic coexistence to continuous transitions.Physical review letters, 114(3):035702, 2015

2015
[24]

Freezing of the classical two-dimensional, one-component plasma

Patricia L Radloff, Biman Bagchi, Charles Cerjan, and Stuart A Rice. Freezing of the classical two-dimensional, one-component plasma. The Journal of chemical physics, 81(3):1406– 1415, 1984. The density profile of a Coulomb plasma on a cylinder 17

1984
[25]

Exact results for the two-dimensional one-component plasma.Physical Review Letters, 46(6):386, 1981

B Jancovici. Exact results for the two-dimensional one-component plasma.Physical Review Letters, 46(6):386, 1981

1981
[26]

Classical coulomb systems near a plane wall

B Jancovici. Classical coulomb systems near a plane wall. i.Journal of Statistical Physics, 28(1):43–65, 1982

1982
[27]

Surface density profile of the one- component plasma

JP Badiali, ML Rosinberg, D Levesque, and JJ Weis. Surface density profile of the one- component plasma. Journal of Physics C: Solid State Physics, 16(11):2183, 1983

1983
[28]

T. Can, P. J. Forrester, G. Téllez, and P. Wiegmann. Singular behavior at the edge of laughlin states. Phys. Rev. B, 89:235137, Jun 2014

2014
[29]

Exact and asymptotic features of the edge density profile for the one component plasma in two dimensions.Journal of Statistical Physics, 158(5):1147–1180, 2015

T Can, PJ Forrester, G Téllez, and P Wiegmann. Exact and asymptotic features of the edge density profile for the one component plasma in two dimensions.Journal of Statistical Physics, 158(5):1147–1180, 2015

2015
[30]

Edge of the laughlin droplet.Physical Review B, 53(16):10906, 1996

Nilanjana Datta, Rudolf Morf, and Ruggero Ferrari. Edge of the laughlin droplet.Physical Review B, 53(16):10906, 1996

1996
[31]

Monte carlo evaluation of trial wave functions for the fractional quantized hall effect: disk geometry.Physical Review B, 33(4):2221, 1986

R Morf and BI Halperin. Monte carlo evaluation of trial wave functions for the fractional quantized hall effect: disk geometry.Physical Review B, 33(4):2221, 1986

1986
[32]

Classical coulomb systems near a plane wall

B Jancovici. Classical coulomb systems near a plane wall. ii.Journal of Statistical Physics, 29(2):263–280, 1982

1982
[33]

Charge fluctuations in the two-dimensional one- component plasma

D Levesque, J-J Weis, and JL Lebowitz. Charge fluctuations in the two-dimensional one- component plasma. Journal of Statistical Physics, 100(1-2):209–222, 2000

2000
[34]

Large-n expansion for the 2d dyson gas.Journal of Physics A: Mathematical and General, 39(28):8933, 2006

A Zabrodin and P Wiegmann. Large-n expansion for the 2d dyson gas.Journal of Physics A: Mathematical and General, 39(28):8933, 2006

2006
[35]

P. A. McClarty and M. A. Moore. Freezing effects in the two-dimensional one-component plasma and in thin-film type-ii superconductors.Phys. Rev. B, 75:172507, May 2007

2007
[36]

Overcrowding and separation estimates for the coulomb gas.Communications on Pure and Applied Mathematics, 77(7):3227–3276, 2024

Eric Thoma. Overcrowding and separation estimates for the coulomb gas.Communications on Pure and Applied Mathematics, 77(7):3227–3276, 2024

2024
[37]

The two-dimensional coulomb gas: fluctuations through a spectral gap.arXiv preprint arXiv:2210.13959, 2022

Yacin Ameur, Christophe Charlier, and Joakim Cronvall. The two-dimensional coulomb gas: fluctuations through a spectral gap.arXiv preprint arXiv:2210.13959, 2022

2022 arXiv
[38]

Universal modeling of oscillations in fractional quantum hall fluids.Physical Review B, 110(7):075113, 2024

Guangyue Ji, Koyena Bose, Ajit C Balram, and Bo Yang. Universal modeling of oscillations in fractional quantum hall fluids.Physical Review B, 110(7):075113, 2024

2024
[39]

Cornering the universal shape of fluctuations

Benoit Estienne, Jean-Marie Stéphan, and William Witczak-Krempa. Cornering the universal shape of fluctuations. Nature Communications, 13(1):287, 2022

2022
[40]

The boundary density profile of a coulomb droplet

Gabriel Cardoso, Jean-Marie Stéphan, and Alexander G Abanov. The boundary density profile of a coulomb droplet. freezing at the edge.Journal of Physics A: Mathematical and Theoretical, 54(1):015002, 2020

2020
[41]

Singular behavior at the edge of laughlin states

T Can, PJ Forrester, G Téllez, and P Wiegmann. Singular behavior at the edge of laughlin states. Physical Review B, 89(23):235137, 2014

2014
[42]

Anomalous hydrodynamics of two-dimensional vortex fluids

Paul Wiegmann and Alexander G Abanov. Anomalous hydrodynamics of two-dimensional vortex fluids. Physical review letters, 113(3):034501, 2014

2014
[43]

Kosterlitz–thouless physics: a review of key issues.Reports on Progress in Physics, 79(2):026001, 2016

J Michael Kosterlitz. Kosterlitz–thouless physics: a review of key issues.Reports on Progress in Physics, 79(2):026001, 2016

2016
[44]

Hypernetted-chain approximation and quasiparticle energies in the (1/3 fractional quantized hall effect.Physical Review B, 36(12):6302, 1987

HA Fertig and BI Halperin. Hypernetted-chain approximation and quasiparticle energies in the (1/3 fractional quantized hall effect.Physical Review B, 36(12):6302, 1987

1987
[45]

K. R. Elder and Martin Grant. Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals.Phys. Rev. E, 70:051605, Nov 2004

2004
[46]

Academic press, 2013

Jean-Pierre Hansen and Ian Ranald McDonald.Theory of simple liquids: with applications to soft matter. Academic press, 2013

2013

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

Statistical Mechanics of Simple Coulomb Systems.Physics Reports- Review Section Of Physics Letters, 59(1):1–94, 1980

M Baus and J P Hansen. Statistical Mechanics of Simple Coulomb Systems.Physics Reports- Review Section Of Physics Letters, 59(1):1–94, 1980

work page 1980

[2] [2]

A monte carlo study of the classical two- dimensional one-component plasma

JM Caillol, D Levesque, JJ Weis, and JP Hansen. A monte carlo study of the classical two- dimensional one-component plasma. Journal of Statistical Physics, 28(2):325–349, 1982

work page 1982

[3] [3]

de Leeuw and J.W

S.W. de Leeuw and J.W. Perram. Statistical mechanics of two-dimensional coulomb systems: Ii. the two-dimensional one-component plasma. Physica A: Statistical Mechanics and its Applications, 113(3):546 – 558, 1982

work page 1982

[4] [4]

Anomalous quantum hall effect: an incompressible quantum fluid with fractionally charged excitations

Robert B Laughlin. Anomalous quantum hall effect: an incompressible quantum fluid with fractionally charged excitations. Physical Review Letters, 50(18):1395, 1983

work page 1983

[5] [5]

Quantum Hall edges beyond the plasma analogy

Per Moosavi, Blagoje Oblak, Bastien Lapierre, Benoit Estienne, and Jean-Marie Stéphan. Quantum hall edges beyond the plasma analogy.arXiv preprint arXiv:2407.19013, 2024

work page Pith review arXiv 2024

[6] [6]

W-infinity symmetry in the quantum hall effect beyond the edge

Andrea Cappelli and Lorenzo Maffi. W-infinity symmetry in the quantum hall effect beyond the edge. Journal of High Energy Physics, 2021(5):1–39, 2021

work page 2021

[7] [7]

Hydrodynamics of euler incompressible fluid and the fractional quantum hall effect

PB Wiegmann. Hydrodynamics of euler incompressible fluid and the fractional quantum hall effect. Physical Review B, 88(24):241305, 2013

work page 2013

[8] [8]

Statistical ensembles of complex, quaternion, and real matrices

Jean Ginibre. Statistical ensembles of complex, quaternion, and real matrices. Journal of Mathematical Physics, 6(3):440–449, 1965

1965