Ising model on nonorientable surfaces: exact solution for the Möbius strip and the Klein bottle
Closed-form expressions are obtained for the partition function of the Ising model on an MxN simple-quartic lattice embedded on a Möbius strip and a Klein bottle. The solutions all lead to the same bulk free energy, but for finite M and N the expressions are different depending on whether the strip...
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Veröffentlicht in: | Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2001-02, Vol.63 (2 Pt 2), p.026107-026107, Article 026107 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | Closed-form expressions are obtained for the partition function of the Ising model on an MxN simple-quartic lattice embedded on a Möbius strip and a Klein bottle. The solutions all lead to the same bulk free energy, but for finite M and N the expressions are different depending on whether the strip width M is odd or even. Finite-size corrections at criticality are analyzed and compared with those under cylindrical and toroidal boundary conditions. Our results are consistent with the conformal field prediction of a central charge c=1/2, provided that the twisted Möbius boundary condition is regarded as a free or fixed boundary. |
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ISSN: | 1539-3755 1063-651X 1095-3787 |
DOI: | 10.1103/PhysRevE.63.026107 |