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Monte Carlo simulation of O(2) phi^4 field theory in three dimensions

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arxiv cond-mat/0103227 v4 pith:O37XNKZY submitted 2001-03-09 cond-mat hep-lat

Peter Arnold , Guy D. Moore This is my paper · ORCID
classification cond-mathep-lat
keywords theoryfieldphasetransitioncarlolatticemontethree-dimensional
verification ladder T0 review T1 audit T2 compute T3 formal
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Using standard numerical Monte Carlo lattice methods, we study non-universal properties of the phase transition of three-dimensional phi^4 theory of a 2-component real field phi = (phi_1,phi_2) with O(2) symmetry. Specifically, we extract the renormalized values of <phi^2>/u and r/u^2 at the phase transition, where the continuum action of the theory is \int d^3x [ (1/2) |\grad\phi|^2 + \half r \phi^2 + {u\over4!} \phi^4 ]. These values have applications to calculating the phase transition temperature of dilute or weakly-interacting Bose gases (both relativistic and non-relativistic). In passing, we also provide perturbative calculations of various O(a) lattice-spacing errors in three-dimensional O(N) scalar field theory, where (a) is the lattice spacing.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Hot news on the phase structure of the SMEFT

    hep-ph 2025-07 conditional novelty 7.0 of 10

    A full O(g^4) dimensional reduction of the dimension-six SMEFT shows that the top-Higgs operator O_tphi can trigger a first-order electroweak phase transition with zero (phi-dagger phi)^3 coupling at zero temperature.

  2. Phase Transitions in Dimensional Reduction up to Three Loops

    hep-ph 2025-05 conditional novelty 7.0 of 10

    In a toy complex-scalar model, 1-loop dimension-6 matching corrections compete with 2-loop quartic corrections and dominate 3-loop thermal-mass corrections for strong phase transitions.

  3. What happens when supercooling is terminated by curvature flipping of the effective potential?

    hep-ph 2024-12 conditional novelty 6.0 of 10

    Supercooling terminated by curvature flipping still proceeds by bubble nucleation and expansion, not by smooth phase mixing, according to 3D lattice simulations.

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