Ising model on nonorientable surfaces: Exact solution for the Moebius strip and the Klein bottle

Abstract

Closed-form expressions are obtained for the partition function of the Ising model on an M x N simple-quartic lattice embedded on a Moebius strip and a Klein bottle for finite M and N. The finite-size effects at criticality are analyzed and compared with those under cylindrical and toroidal boundary conditions. Our analysis confirms that the central charge is c=1/2.

8 pages, 3 eps figures

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