The Schwinger and Thirring models at finite chemical potential and temperature

We study the generating functional for the massless Schwinger model in the torus, at nonzero chemical potential and temperature. The lack of hermiticity of the Dirac operator yields a non-trivial phase in the effective action, which is a topological contribution induced by the chemical potential. In the sector with no zero modes, we evaluate exactly the generating functional, the partition function, the boson propagator and the thermally averaged Polyakov loop. The system bosonizes at finite T and \mu, with the same mass as in vacuum. From the solution obtained for the Schwinger model we derive also exactly the generating functional and the partition function for the massless Thirring model at nonzero T and \mu.