Finite Size Scaling of Probability Distributions in SU(2) Lattice Gauge Theory and Phi^4 Field Theory

TL;DR

This paper demonstrates that the finite size scaled probability distributions of the order parameter in SU(2) lattice gauge theory and phi^4 field theory are identical, supporting their shared universality class and showcasing a method for analyzing phase transitions.

Contribution

It introduces a method of comparing finite size scaled probability distributions in different models to identify universality classes, specifically linking SU(2) gauge theory to the Ising class.

Findings

Distributions are identical for both models

Supports SU(2) in the Ising universality class

Method can be applied to other phase transition studies

Abstract

For a system near a second order phase transition, the probability distribution for the order parameter can be given a finite size scaling form. This fact is used to compare the finite temperature phase transition for the Wilson lines in d=3+1 SU(2) lattice gauge theory with the phase transition in d=3 phi^4 field theory. I exhibit the finite size scaled probability distributions in the form of a function of two variables (the reduced `temperature' and the magnetization) for both models. The two surfaces look identical, and an analysis of the errors also suggests that they are the same. This strengthens the idea that the SU(2) effective line theory is in the Ising universality class. I argue for the wider application of the method used here.