We study the finite-temperature phase transition of the generalized
Gross-Neveu model with continous chiral symmetry in 2<d≤4 euclidean
dimensions. The critical exponents are computed to the leading order in the
1/N expansion at both zero and finite temperatures. A dimensionally reduced
theory is obtained after the introduction of thermal counterterms necessary to
cancel thermal divergences that arise in the limit of high temperature.
Although at zero temperature we have an infinitely and continously degenerate
vacuum state, we show that at finite temperature this degeneracy is discrete
and, depending on the values of the bare parameters, we may have either total
or partial restoration of symmetry. Finally we determine the universality class
of the reduced theory by a simple analysis of the infrared structure of
thermodynamic quantities computed using the reduced action as starting point.Comment: Latex, 25 pages, 4 eps fig., uses epsf.sty and epsf.te
