Finite-size scaling and asymptotic freedom of the SU(2) lattice gauge model

Abstract

The dependence of the plaquette energy on lattice size $L^4$ for the four-dimensional SU(2) lattice gauge model is obtained in the crossover region by Monte Carlo calculations for $L=4\mathrm{} \mathrm{to} 10$. Extending finite-size scaling theory to non-Abelian gauge models, a fit to the data verifies the validity of scaling and asymptotic freedom. The value obtained for the coefficient ${\gamma }_0$ in the beta function, corresponding to the one-loop term in perturbation theory, is ${\gamma }_0=0.041\mathrm{}$, in good agreement with the result of SU(2) gauge field theory, ${\gamma }_0=\frac{11}{24{\pi }^2}=0.046\mathrm{}\dots$. We estimate an upper bound to the glueball mass $m\cong 1.2\sqrt{\kappa }$ where $\kappa$ is the string tension.