Mass generation without symmetry breakdown in the chiral Gross-Neveu model at finite temperature and finite N in 2+1 dimensions

The chiral Gross-Neveu model is one of the most popular toy models for QCD being a generic testing field for many ideas in particle physics. It has been studied in the past in detail in the limit of infinite number of flavors of fermions. Quite astonishingly, the study of this model was not carried through in all its facets. The most important omission is the study of the onset of quasi-long-range order in the decoupled massless phase field. The present work eliminates this deficiency. In this paper we derive behavior of the Kosterlitz-Thouless transition in this model at finite temperature in 2 + 1 dimensions in the regime when the number N of field components is large but finite. We also prove the anticipated before key feature of the model, namely, that in the regime of infinite N the temperature of the Kosterlitz-Thouless transition merges with the critical temperature T*, given by a mean-field equation for the gap modulus, thus recovering the "BCS-like" scenario [(T* - T-KT)/T* --> 0] of the phase transition at N --> infinity. (C) 2001 Published by Elsevier Science B.V.