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

Abstract

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 $T^{\ast }$. That is, at small N, along with a quasiordered phase $0<T<T_{KT}$ the system possesses a very large region of precursor fluctuations $T_{KT}<T<T^{\ast }$ which disappear only at a temperature $T^{\ast }$, substantially higher than the temperature $T_{KT}$ of Kosterlitz-Thouless transition.

a factor 2 corrected. An extended discussion of similarities and differences of low-N behavior of the chiral GN model and various models of superconductivity is currently in preparation and will be presented in additional article

References in corpus (2)

• Nonlinear sigma model approach for chiral fluctuations and symmetry breakdown in Nambu-Jona-Lasinio model
• No Spontaneous Breakdown of Chiral Symmetry in Nambu-Jona-Lasinio Model

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