The role of the lattice asymmetry parameter xi in the phase structure
description of SU(2) and SU(3) gluodynamics at finite temperature in t
he SU(N) similar or equal to Z(N) approach has been studied analytical
ly. The properties of thermodynamic quantities have been investigated
near the physical border. The effective action which includes the firs
t nontrivial order from the spacelike part allows estimates to be made
of the phase structure not only close to the physical border but in t
he whole area of couplings. We find that thermodynamic quantities depe
nd on xi and this dependence may be strong enough, up to discontinuity
over this parameter for some of them. [S0556-2821(97)04323-3].