Non-perturbative beta-function in SU(2) lattice gauge fields thermodynamics

The new method of nonperturbative calculation of the beta function in the lattice gauge theory is proposed. The method is based on the finite size scaling hypothesis. Monte Carlo simulations of SU(2) lattice gauge theory have shown that there are rather large deviations from asymptotic scaling behaviour in the range of coupling constants accessible with today’s computing power. This raised the question of whether we are able to see continuum physics in these simulations. The answer requires the knowledge of the β-function away from the asymptotic regime where it is dominated by the two leading terms in its perturbative expansion (g-coupling constant) βf (g) = −b0g − b1g5 − . . . , (1) where b0 = 11 24π , b1 = 17 96π . During the last years a large effort has been put into the numerical determination of the β-function for the lattice gauge theories by measuring the deviation from the two-loop β-function (1) [1,2]. We propose a new method of determination of the nonperturbative β-function, which is based on the finite size scaling hypothesis. We consider SU(2) gauge theory at finite temperature on N σ ×Nτ lattices with the standard Wilson action S(U) = 4 g ∑