Continuum study of various susceptibilities within thermal ${\mathbf{QED}}_3$

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 the 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.

Figure 1

Dependence of the chiral susceptibility ${\chi }^c$ on temperature $T$.

Figure 2

Dependence of the fermion number susceptibility ${\chi }^n/{\chi }_f^n$ on temperature $T$, where ${\chi }_f^n$ is the free fermion number susceptibility at finite temperature.

Figure 3

Dependence of the thermal susceptibility ${\chi }^T$ on temperature $T$.

Figure 4

Dependence of the staggered spin susceptibility ${\chi }^s$ on temperature $T$.

Figure 5

Dependence of the chiral susceptibility ${\chi }^c$ on temperature $T$ for several $m$.

Figure 6

Dependence of the fermion number susceptibility ${\chi }^n/{\chi }_f^n$ on temperature $T$ for several $m$, where ${\chi }_f^n$ is the free fermion number susceptibility at finite temperature and current mass of the fermion.

Figure 7

Dependence of the thermal susceptibility ${\chi }^T$ on temperature $T$ for several $m$.

Figure 8

Dependence of the staggered spin susceptibility ${\chi }^s$ on temperature $T$ for several $m$.