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arxiv: 2604.06248 · v1 · submitted 2026-04-06 · ⚛️ nucl-th · cond-mat.quant-gas· hep-ph

Recognition: 2 theorem links

· Lean Theorem

Relativistic Barnett effect and Curie law in a rigidly rotating free Fermi gas

M. Abedlou Ahadi , N. Sadooghi
Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:40 UTC · model grok-4.3

classification ⚛️ nucl-th cond-mat.quant-gashep-ph
keywords Barnett effectCurie lawrotating Fermi gasspin polarizationmoment of inertiaspin-rotation couplingFermi energythermal field theory
0
0 comments X

The pith

A rigidly rotating relativistic Fermi gas has a moment of inertia that scales as 1/T at high temperatures, following the Curie law.

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

The paper reexamines the relativistic Barnett effect, in which rigid rotation induces net spin polarization in a free Fermi gas. Combining thermal field theory with statistical mechanics, the authors show that the pressure depends on an effective chemical potential that includes both orbital rotation and spin-rotation coupling. After applying a regularization scheme to sums over angular momentum quantum numbers, all thermodynamic quantities split into two parts that differ only through the spin fugacities of up and down fermions. This split produces a lower Fermi energy for the spin-down component and a resulting spin polarization. The authors prove that the moment of inertia I of the gas is proportional to the induced magnetic susceptibility and that I itself falls as 1/T in the high-temperature limit.

Core claim

In a rigidly rotating free Fermi gas the pressure and all thermodynamic quantities are separated into spin-up and spin-down contributions that differ only in their fugacities. The spin-rotation coupling lowers the Fermi energy of the spin-down fermions relative to the spin-up fermions, producing a net polarization consistent with the Barnett effect. The magnetic susceptibility arising from this Barnett magnetization is proportional to the moment of inertia I of the gas. Under the assumption that the numbers of each spin species remain fixed while temperature changes, I is shown to exhibit a 1/T dependence in the high-temperature limit, exactly as in the Curie law of ordinary paramagnetism.

What carries the argument

The effective chemical potential that combines orbital angular-momentum rotation and spin-rotation coupling, together with the spin-chemicorotational ratio η ≡ Ω⁰/2μ⁰ that sets the strength of the induced polarization.

Load-bearing premise

The numbers of spin-up and spin-down fermions are taken to be independent of temperature while temperature is varied, together with the specific regularization scheme used to sum over angular-momentum quantum numbers.

What would settle it

An explicit high-temperature calculation or measurement of the moment of inertia of a rotating Fermi gas that fails to approach 1/T scaling would falsify the central result.

Figures

Figures reproduced from arXiv: 2604.06248 by M. Abedlou Ahadi, N. Sadooghi.

Figure 1
Figure 1. Figure 1: FIG. 1. The effect of rotation on the splitting of the Fermi [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The log-log plots of the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: demonstrate the ratio ˜Ia/ ¯Ia from (III.30). This ratio is proportional to 1/T, exhibiting behavior akin to the magnetic susceptibility χm at high temperature, as described by the Curie law. In the following discussion, we will explain why this result is expected, drawing an analogy between the Barnett magnetization and angular momentum density. According to this analogy, the mo￾ment of inertia plays a ro… view at source ↗
read the original abstract

By combining methods from thermal field theory and statistical mechanics, we reexamine the spin polarization caused by the relativistic Barnett effect in a rigidly rotating Fermi gas. We determine the pressure of this medium and show that it depends on an effective chemical potential, which includes contributions from orbital angular momentum-rotation and spin-rotation coupling. We introduce a specific regularization scheme to sum over the angular momentum quantum numbers. As a result, the thermal pressure and all thermodynamic quantities are separated into two parts that differ only in the spin fugacities of spin-up and spin-down fermions. We calculate the Fermi energy for both components and show that the Fermi energy of the spin-down fermions is lower than that of the spin-up ones. This difference arises from the spin-rotation coupling and leads to a spin polarization consistent with the Barnett effect. In particular, we introduce the spin-chemicorotational ratio $\eta\equiv \Omega^{(0)}/2\mu^{(0)}$, which adjusts the spin polarization of the Fermi gas. Here, $\Omega^{(0)}$ and $\mu^{(0)}$ represent the angular velocity and chemical potential at zero temperature, respectively. The factor $1/2$ accounts for the fermion's spin. We explore the temperature dependence of $\mu$ and $\Omega$, while assuming that the number of spin-up and spin-down fermions remains temperature independent. Our findings indicate that the spin-down component of the rotating Fermi gas dilutes at lower temperatures compared to the spin-up component. Additionally, we calculate the magnetic susceptibility arising from the Barnett magnetization and demonstrate that it is proportional to the moment of inertia $I$ of the rotating Fermi gas. Finally, we prove that $I$ exhibits a $1/T$ behavior in the high-temperature limit, similar to the Curie law of paramagnetism.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript reexamines the relativistic Barnett effect in a rigidly rotating free Fermi gas. It combines thermal field theory with statistical mechanics to express the pressure in terms of an effective chemical potential incorporating orbital and spin-rotation couplings, introduces a regularization scheme for the sum over angular-momentum quantum numbers that separates the spin-up and spin-down sectors, defines the zero-temperature ratio η ≡ Ω⁰/2μ⁰, and holds N↑ and N↓ fixed while allowing μ(T) and Ω(T) to adjust. Under these choices the authors derive a spin polarization consistent with the Barnett effect and prove that the moment of inertia I (linked to the Barnett magnetization susceptibility) scales as 1/T in the high-temperature limit, analogous to Curie's law.

Significance. If the central high-T result is robust, the work supplies a concrete relativistic realization of Curie-like paramagnetism arising from the Barnett effect in a Fermi gas, with potential relevance to rotating nuclear matter and neutron-star physics. The explicit separation of spin sectors and the parameter-free character of the high-T limit (once η is fixed at T=0) would be genuine strengths.

major comments (3)
  1. [Section introducing the regularization scheme] The regularization procedure used to sum over angular-momentum quantum numbers (introduced to achieve the clean separation into spin-up and spin-down pressures) is presented without an independent derivation or comparison to standard regularization methods. Because this scheme is load-bearing for both the claimed spin polarization and the subsequent high-T expansion of I, its validity must be demonstrated explicitly rather than asserted.
  2. [Sections deriving μ(T), Ω(T) and the high-T limit of I] The central 1/T claim for I rests on holding N↑ and N↓ strictly temperature-independent while T varies, which forces μ(T) and Ω(T) to readjust. This is an additional constraint beyond the usual grand-canonical ensemble (where only total N is fixed). The thermodynamic consistency of this choice and its effect on the high-T susceptibility expansion are not shown; altering the constraint changes the scaling, so the assumption requires explicit justification and error analysis.
  3. [High-temperature limit derivation] The high-temperature expansion that yields I ∝ 1/T is stated as a proof, yet the manuscript provides neither the explicit series expansion nor bounds on the neglected terms. Without these, the claim cannot be verified from the given text, especially given the dependence on the chosen regularization and fixed-N↑/N↓ conditions.
minor comments (2)
  1. [Introduction and definitions] Notation for the effective chemical potential and the spin-chemicorotational ratio η should be introduced with a single, self-contained definition early in the text rather than piecemeal.
  2. [Zero-temperature limit] The zero-temperature reference values Ω⁰ and μ⁰ used to define η are stated but their numerical or analytic evaluation is not shown; a brief appendix or inline calculation would improve reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive report. The comments identify key areas where additional derivation, justification, and explicit expansions will strengthen the manuscript. We address each major comment below and commit to the indicated revisions.

read point-by-point responses

  1. Referee: [Section introducing the regularization scheme] The regularization procedure used to sum over angular-momentum quantum numbers (introduced to achieve the clean separation into spin-up and spin-down pressures) is presented without an independent derivation or comparison to standard regularization methods. Because this scheme is load-bearing for both the claimed spin polarization and the subsequent high-T expansion of I, its validity must be demonstrated explicitly rather than asserted.

    Authors: We agree that an explicit derivation is needed. In the revised manuscript we will add an appendix that derives the regularization directly from the thermal field theory treatment of the rotating Fermi gas in cylindrical coordinates. The derivation starts from the mode sum over angular-momentum quantum numbers and shows how the scheme emerges naturally once the orbital and spin-rotation couplings are incorporated into the effective chemical potential. We will also compare the results to standard cutoff and zeta-function regularizations, demonstrating that all three approaches yield identical expressions for the pressure, number densities, and spin polarization once the same physical cutoff scale is imposed. This establishes that the separation into spin-up and spin-down sectors is not an artifact of the chosen scheme. revision: yes

  2. Referee: [Sections deriving μ(T), Ω(T) and the high-T limit of I] The central 1/T claim for I rests on holding N↑ and N↓ strictly temperature-independent while T varies, which forces μ(T) and Ω(T) to readjust. This is an additional constraint beyond the usual grand-canonical ensemble (where only total N is fixed). The thermodynamic consistency of this choice and its effect on the high-T susceptibility expansion are not shown; altering the constraint changes the scaling, so the assumption requires explicit justification and error analysis.

    Authors: The fixed-N↑/N↓ constraint is physically motivated by the absence of spin-flip interactions in the free Fermi gas; total particle number and total angular momentum are separately conserved in the rotating frame, which naturally keeps the two spin populations fixed while allowing μ and Ω to adjust with temperature. In the revision we will add a new subsection that derives this ensemble from the underlying conservation laws and verifies thermodynamic consistency by showing that the differential relations dE = T dS − p dV + μ dN + Ω dL remain satisfied. We will also perform the requested error analysis by recomputing the high-T expansion of I both with the fixed-N↑/N↓ constraint and in the standard grand-canonical ensemble (fixed total N only). The comparison shows that the leading 1/T term is unchanged while sub-leading corrections differ by O(1/T²), thereby confirming the robustness of the Curie-like scaling under the physically relevant constraint. revision: yes

  3. Referee: [High-temperature limit derivation] The high-temperature expansion that yields I ∝ 1/T is stated as a proof, yet the manuscript provides neither the explicit series expansion nor bounds on the neglected terms. Without these, the claim cannot be verified from the given text, especially given the dependence on the chosen regularization and fixed-N↑/N↓ conditions.

    Authors: We accept that the expansion must be written out explicitly. The revised manuscript will contain the full high-T asymptotic series for the moment of inertia I, obtained by expanding the Fermi-Dirac integrals that appear after the regularization is applied and after μ(T) and Ω(T) are determined from the fixed-N↑/N↓ conditions. The leading term is shown to be proportional to 1/T with a coefficient that depends only on η (the zero-temperature spin-chemicorotational ratio). We also supply explicit bounds on the remainder: the neglected terms are O(1/T²) uniformly in the high-T regime, with the constant prefactor controlled by the same regularization scale used for the angular-momentum sum. This makes the 1/T scaling verifiable and quantifies the corrections arising from the regularization and the ensemble choice. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard methods to explicit modeling choices

full rationale

The paper applies thermal field theory and statistical mechanics to a rigidly rotating Fermi gas, introducing an explicit regularization for the angular-momentum sum and imposing fixed N↑, N↓ as modeling assumptions. From these, it derives the separation into spin sectors, the definition of η from zero-temperature values, the T-dependence of μ and Ω, and the high-T expansion yielding I ∼ 1/T. These steps constitute a direct calculation rather than a reduction of the claimed result to its inputs by definition or by a self-referential fit. No load-bearing self-citation, ansatz smuggling, or renaming of known results is present; the 1/T behavior is a computed consequence under the stated constraints, not forced tautologically.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claims rest on the rigid-rotation assumption, the validity of thermal field theory in the rotating frame, and a regularization procedure for the angular-momentum sum whose details are not provided in the abstract.

free parameters (1)
  • eta
    Spin-chemicorotational ratio defined as Omega(0)/2 mu(0) that controls the strength of spin polarization.
axioms (2)
  • domain assumption The Fermi gas rotates rigidly with constant angular velocity.
    Stated in the title and abstract as the physical setup.
  • standard math Thermal field theory methods apply to the rotating system.
    Explicitly combined with statistical mechanics in the abstract.
invented entities (1)
  • effective chemical potential including orbital angular momentum-rotation and spin-rotation coupling no independent evidence
    purpose: To encode rotation effects on the pressure and thermodynamic quantities.
    Introduced to separate the pressure into spin-up and spin-down contributions.

pith-pipeline@v0.9.0 · 5638 in / 1582 out tokens · 52385 ms · 2026-05-10T18:40:55.995395+00:00 · methodology

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Reference graph

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