Continuum study of various susceptibilities within thermal QED$_3$

TL;DR

This study examines four different susceptibilities in thermal QED3 using Dyson-Schwinger equations, revealing their behaviors near phase transitions and the limitations of some susceptibilities in describing crossovers.

Contribution

It provides a comprehensive numerical analysis of multiple susceptibilities in thermal QED3, highlighting differences in their critical behaviors beyond the chiral limit.

Findings

All four susceptibilities indicate the same critical temperature in the chiral limit.

Beyond the chiral limit, susceptibilities show different critical temperatures, suggesting a crossover region.

Fermion number and staggered spin susceptibilities lose singular behavior, limiting their use in describing crossovers.

Abstract

In this paper, the relations of four different susceptibilities (i.e., the chiral susceptibility, the fermion number susceptibility, the thermal susceptibility and the staggered spin susceptibility) are investigated both in and beyond the chiral limit. To this end, we numerically solve the finite temperature version of the truncated Dyson-Schwinger equations for fermion and boson propagator. It is found that, in the chiral limit, the four susceptibilities give the same critical temperature and signal a typical second order phase transition. But the situation changes beyond the chiral limit: the critical temperatures from the chiral and the thermal susceptibilities are different, which shows that to define a critical region instead of an exclusive point for crossover might be a more suitable choice; meanwhile, both the fermion number and the staggered spin susceptibilities have no singular behaviors any more, this may mean that they are no longer available to describe the crossover properties of the system.