Critical Temperature and Amplitude Ratios from a Finite-Temperature Renormalization Group

TL;DR

This paper employs a finite-temperature renormalization group approach to study the ^4 theory, deriving critical temperature and universal amplitude ratios, and comparing them with three-dimensional Ising model results.

Contribution

It introduces a perturbative, divergence-free flow equation method using a fiducial temperature as a flow parameter for finite-temperature ^4 theory.

Findings

Critical temperature as a function of zero-temperature parameters

Universal amplitude ratios connecting broken and symmetric phases

Good agreement with 3D Ising model results

Abstract

We study $\l\f^4$ theory using an environmentally friendly finite-temperature renormalization group. We derive flow equations, using a fiducial temperature as flow parameter, develop them perturbatively in an expansion free from ultraviolet and infrared divergences, then integrate them numerically from zero to temperatures above the critical temperature. The critical temperature, at which the mass vanishes, is obtained by integrating the flow equations and is determined as a function of the zero-temperature mass and coupling. We calculate the field expectation value and minimum of the effective potential as functions of temperature and derive some universal amplitude ratios which connect the broken and symmetric phases of the theory. The latter are found to be in good agreement with those of the three-dimensional Ising model obtained from high- and low-temperature series expansions.