Finite Temperature Schwinger Model

TL;DR

This paper calculates the temperature dependence of the chiral condensate in the Schwinger model using a finite torus approach, deriving analytic expressions valid at any temperature and revealing exponential decay at high temperatures.

Contribution

It provides an analytic form of the chiral condensate at finite temperature in the Schwinger model, including high-temperature behavior, using a finite torus Euclidean approach.

Findings

Analytic expression for the chiral condensate at any temperature.

High-temperature behavior shows exponential decay of the condensate.

Derived Green functions and Wilson loop correlators on the torus.

Abstract

The temperature dependence of the order parameter of the Schwinger model is calculated in the euclidean functional integral approach. For that we solve the model on a finite torus and let the spatial extension tend to infinity at the end of the computations. The induced actions, fermionic zero-modes, relevant Green functions and Wilson loop correlators on the torus are derived. We find the analytic form of the chiral condensate for any temperature and in particular show that it behaves like \< \bar\Psi\Psi \> \sim -2 T\exp(-\pi\sqrt{\pi}T/e) for temperatures large compared to the induced photon mass.