Precise Phase Structure in Four-fermion Interaction Model on Torus

Abstract

We investigate finite-size effects on chiral symmetry breaking in a four-fermion interaction model at finite temperature and chemical potential. Following the imaginary time formalism, the thermal quantum field theory is constructed on an S 1 imaginary time direction. In this paper, the finite-size effect is introduced by a compact S 1 spatial direction with a U (1)-valued boundary condition. Thus we study the model on a R D−2 × S 1 × S 1 torus. Phase diagrams are obtained by evaluating local minima of the effective potential in the leading order of the 1/N expansion. From the grand potential, we calculate the particle number density and the pressure and show the correspondence with the phase structure. We obtain a stable size where the sign of the pressure flips from negative to positive as the size decreases. It is found that the finite chemical potential expands the parameter range for which the stable size exists.