Properties of solutions by the Schwinger-Dyson equation at finite temperature and density – A four-fermion interaction model –

In this paper, we examine the properties of the solutions obtained by the Schwinger-Dyson equation (SDE). As a simple example, we consider a two-dimensional model including four-fermion interaction. It is shown that when this model is solved by an iterative method using the SDE at finite density, multiple solutions depending on the initial input values are obtained. We investigate the reasons for this situation by examining the convergence of the solutions obtained by iterative method. We also consider the solution of the SDE using alternative methods. Furthermore, we compare these results with analytical solutions at zero temperature and discuss the relation with the behavior of the effective potential. We extend these considerations to finite temperatures. Based on these analyses, we consider ways to avoid spurious solutions that appear in the iterative method.