Aspects of quasi-phase-structure of the Schwinger model on a cylinder with broken chiral symmetry

We consider the Nf-flavour Schwinger Model on a thermal cylinder of circumference beta = 1/T and of finite spatial length L. On the boundaries x(1) = 0 and x(1) = L the fields are subject to an element of a one-dimensional class of bag-inspired boundary conditions which depend on a real parameter theta and break the axial flavour symmetry. For the cases N-integral = 1 and N-integral = 2 all integrals can be performed analytically. While general theorems do not allow for a nonzero critical temperature, the model is found to exhibit a quasi-phase-structure: For finite L the condensate-seen as a function of log(T)-stays almost constant up to a certain temperature (which depends on L), where it shows a sharp crossover to a value which is exponentially close to zero. In the limit L --> infinity the known behaviour for the one-flavour Schwinger model is reproduced. In case of two flavours direct pictorial evidence is given that the theory undergoes a phase-transition at T-c = 0. The latter is confirmed-as predicted by Smilga and Verbaarschot-to be of second order but for the critical exponent delta the numerical value is found to be 2 which is at variance with their bosonization-rule based result delta = 3. (C) 1999 Academic Press.