Aspects of Quasi-Phasestructure of the Schwinger Model on a Cylinder with Broken Chiral Symmetry

Details Aspects of Quasi-Phasestructure of the Schwinger Model on a Cylinder with Broken Chiral Symmetry Aspects of Quasi-Phasestructure of the Schwinger Model on a Cylinder with Broken Chiral Symmetry

1998-05-19

arxiv.org/abs/hep-th/9805124v2

Annals Phys. 273 (1999) 1-36

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 29 pages, uses epsfig, error in discussion corrected

Scientific paper

10.1006/aphy.1998.5894

We consider the N_f-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 $N_f=1$ and $N_f=2$ 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 $L \to \infty$ 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 prediction $\delta=3$.

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