Mass generation without phase coherence in the Chiral Gross-Neveu Model at finite temperature and small N in 2+1 dimensions

The chiral Gross-Neveu model is one of the most popular toy models for QCD. In the past, it has been studied in detail in the large-N limit. In this paper we study its small-N behavior at finite temperature in 2+1 dimensions. We show that at small N the phase diagram of this model is {\it principally} different from its behavior at $N\to \infty$. We show that for a small number $N$ of fermions the model possesses two characteristic temperatures $T_{KT}$ and $T^*$. That is, at small N, along with a quasiordered phase $0<T<T_{KT}$ the system possesses a very large region of precursor fluctuations $T_{KT}<T<T^*$ which disappear only at a temperature $T^*$, substantially higher than the temperature $T_{KT}$ of Kosterlitz-Thouless transition.