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

Abstract

We determine the critical point and the ratios $β/ν$ and $γ/ν$ of critical exponents of the deconfinement transition in $SU(2)$ gauge theory by applying the $χ^2$-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 $ω=1\pm0.1$. From the derivatives of the Polyakov loop dependent quantities we estimate then $1/ν$. The result from the derivative of $g_r$ is $1/ν=0.63\pm0.01$, in complete agreement with that of the $3d$ Ising model.