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.

Comments: 32 pages