Three types of boundary conditions in a four-fermion interacting model for quarks

Abstract

In this note, we study the phase transition of an effective four-fermion model describing interactions between quarks, taking into account finite size and chemical potential effects on the system, with periodic, quasi-periodic, and anti-periodic boundary conditions in D - Euclidean dimensions through Jacobi theta functions. Strictly speaking, this is performed by the generalized Matsubara formalism and the Schwinger proper-time representation. We consider the system at temperature T and the spatial coordinates compacted along the direction j with length Lj. The gap equation of the system is solved numerically and we investigate its behavior when the thermodynamic parameters of the model are changed.