# Finite Size Scaling and Universality in SU(2) at Finite Temperature

## TL;DR

This study investigates the finite size scaling and universality class of SU(2) gauge theory at finite temperature by analyzing the Binder cumulant across different lattice sizes, finding results consistent with the 3D Ising model.

## Contribution

The paper provides a new estimate of the critical exponent nu for SU(2) gauge theory and explores the effects of rotational symmetry breaking on finite size scaling.

## Key findings

- Estimated nu=0.637(11) consistent with 3D Ising universality
- Identified correction term proportional to N_sigma^{-2.03(4)}
- Results support universality and finite size scaling hypotheses

## Abstract

We study the 4-th Binder cumulant on $4\times{N_\sigma}^3$ lattices for a pure SU(2) gauge theory. We use 20 data points for a sequence of ${N_\sigma}$ in $\beta$ intervals shrinking when ${N_\sigma}$ increases, in order to reduce the nonlinear effects. Using a log-log fit of the slope versus ${N_\sigma}$, we obtain the preliminary result $\nu=0.637(11)$ in reasonably good agreement with the value for the 3D Ising model universality class. The corrections due to irrelevant directions appear to be dominated by a term proportional to ${N_\sigma}^{-2.03(4)}$ which seems compatible with the breaking of rotational symmetry.