# Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the $\chi^2$-method

## TL;DR

This paper precisely determines the critical point and critical exponents of the deconfinement transition in SU(2) gauge theory using a $ ext{chi}^2$-method on Monte Carlo data, confirming universality with the 3D Ising model.

## Contribution

It introduces a $ ext{chi}^2$-method application to analyze critical behavior in SU(2) lattice gauge theory, providing accurate critical parameters and confirming universality class.

## Key findings

- Universal Binder cumulant value at criticality: -1.403(16)
- Next-to-leading exponent $oldsymbol{\omega=1 extpm0.1}$
- Critical exponent ratio $oldsymbol{1/
u=0.63 extpm0.01}$

## Abstract

We determine the critical point and the ratios $\beta/\nu$ and $\gamma/\nu$ of critical exponents of the deconfinement transition in $SU(2)$ gauge theory by applying the $\chi^2$-method to Monte Carlo data of the modulus and the square of the Polyakov loop. With the same technique we find from the Binder cumulant $g_r$ its universal value at the critical point in the thermodynamical limit to $-1.403(16)$ and for the next-to-leading exponent $\omega=1\pm0.1$. From the derivatives of the Polyakov loop dependent quantities we estimate then $1/\nu$. The result from the derivative of $g_r$ is $1/\nu=0.63\pm0.01$, in complete agreement with that of the $3d$ Ising model.