Scaling in a toy model of gluodynamics at finite temperatures

Abstract

In the limit of $\xi \simeq a_\sigma /a_\tau \to \infty $ the gluodynamics without the magnetic part of action ($S_M\sim 1/\xi $) is considered as a self-contained model. The model is studied analytically in the continuum limit on an extremely large lattice ($N_\tau \to \infty $). Scaling conditions for critical temperature and string tension are considered. The model shows trivial ($g^2\sim a_\tau $) asymptotic freedom in the case of continuous gauge groups and nontrivial one ($g^2\sim 1/\ln 1/a_\tau $) for discrete groups.