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Main Authors: Tanaka, Hidekazu, Sasagawa, Shuji
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2503.21034
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author Tanaka, Hidekazu
Sasagawa, Shuji
author_facet Tanaka, Hidekazu
Sasagawa, Shuji
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_21034
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Properties of solutions by the Schwinger-Dyson equation at finite temperature and density : A four-fermion interaction model
Tanaka, Hidekazu
Sasagawa, Shuji
High Energy Physics - Phenomenology
High Energy Physics - Theory
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.
title Properties of solutions by the Schwinger-Dyson equation at finite temperature and density : A four-fermion interaction model
topic High Energy Physics - Phenomenology
High Energy Physics - Theory
url https://arxiv.org/abs/2503.21034