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

We determine the critical point and the ratios $\beta \mathrm{/}\nu$ and $\gamma \mathrm{/}\nu$ 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 $\omega =1\pm 0.1$. From the derivatives of the Polyakov loop dependent quantities we estimate then $1\mathrm{/}\nu$. The result from the derivative of $g_r$ is $1\mathrm{/}\nu =0.63\pm 0.01$, in complete agreement with that of the $3d$ Ising model.