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

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 $\omega =1\pm 0.1$. From the derivatives of the Polyakov loop dependent quantities we estimate then $1/\nu$. The result from the derivative of $g_r$ is $1/\nu =0.63\pm 0.01$, in complete agreement with that of the $3d$ Ising model.

Comments: 11 pages, 3 Postscript figures, uses Plain Tex