Precise phase structure in a four-fermion interaction model on a torus

Abstract

Abstract We investigate finite-size effects on chiral symmetry breaking in a four-fermion interaction model at finite temperature and chemical potential. Applying the imaginary-time formalism, the thermal quantum field theory is constructed on an S1 in the imaginary-time direction. In this paper, the finite-size effect is introduced by a compact S1 spatial direction with a U(1)-valued boundary condition. Thus, we study the model on an $\mathbb {R}^{D-2} \times S^{1} \times S^{1}$ torus. Phase diagrams are obtained by evaluating the 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; then we illustrate the correspondence with the phase structure. We obtain a stable size for which the sign of the pressure flips from negative to positive as the size decreases. Furthermore, the finite chemical potential expands the parameter range over which the stable size exists.