Phase fluctuations in low-dimensional Gross-Neveu models

We consider the Gross-Neveu model with a continuous chiral symmetry in two and three spacetime dimensions at zero and finite temperature. In order to study long-range phase coherence, we construct an effective low-energy Lagrangian for the phase $\theta$. This effective Lagrangian is used to show that the fermionic two-particle correlation function at finite temperature decays algebraically in 2+1 dimensions and exponentially in 1+1 dimensions.