Field theory of finite-size effects for systems with a one-component order parameter

A. Esser, V. Dohm and X.S. Chen

Physica A: Statistical Mechanics and its Applications, 1995, vol. 222, issue 1, 355-397

Abstract: The field-theoretic renormalization-group approach is used to describe finite-size effects near the critical point of the ϕ4 model with a one-component order parameter. Problems of previous perturbation approaches for T < Tc are discussed and an improved perturbation theory is employed that is applicable both above and below Tc. The susceptibility, order parameter, specific heat, and a cumulant ratio are calculated for fixed d < 4 in one-loop order for the case of a cube with periodic boundary conditions. Finite-size scaling functions are evaluated in three dimensions without using the ε = 4 − d expansion. Quantitative agreement with Monte-Carlo (MC) data of the three-dimensional Ising model is found in most cases. Additional MC data of larger systems would be desirable in order to test the detailed predictions of the finite-size field theory more conclusively in the asymptotic region.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:222:y:1995:i:1:p:355-397

DOI: 10.1016/0378-4371(95)00264-2

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