Scaling in a toy model of gluodynamics at finite temperatures

Abstract

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