IR-Divergence and Anomalous Temperature Dependence of the Condensate in the Quenched Schwinger Model

Details IR-Divergence and Anomalous Temperature Dependence of the Condensate in the Quenched Schwinger Model IR-Divergence and Anomalous Temperature Dependence of the Condensate in the Quenched Schwinger Model

1999-02-05

arxiv.org/abs/hep-lat/9902007v4

Phys.Rev. D62 (2000) 034506

Physics

High Energy Physics

High Energy Physics - Lattice

Revtex, 15pp, 1 figure; two references corrected, to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.62.034506

The Schwinger model is used to study the artifacts of quenching in a controlled way. The model is solved on a finite-temperature cylinder of circumference $\beta=1/T$ with bag-inspired local boundary conditions at the two ends $x^1=0$ and $x^1=L$ which break the $\gamma_5$-invariance and thus play the role of a small quark mass. The quenched chiral condensate is found to diverge exponentially as $L\to\infty$, and to diverge (rather than melt as for $N_{\rm f}\geq1$) if the high-temperature limit $\beta\to0$ is taken at finite box-length $L$. We comment on the generalization of our results to the massive quenched theory, arguing that the condensate is finite as $L\to\infty$ and proportional to $1/m$ up to logarithms.

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