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Finite Size Corrections for the Ising Model on Higher Genus Triangular Lattices

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Abstract

We study the topology dependence of the finite size corrections to the Ising model partition function by considering the model on a triangular lattice embedded on a genus two surface. At criticality we observe a universal shape dependent correction, expressible in terms of Riemann theta functions, that reproduces the modular invariant partition function of the corresponding conformal field theory. The period matrix characterizing the moduli parameters of the limiting Riemann surface is obtained by a numerical study of the lattice continuum limit. The same results are reproduced using a discrete holomorphic structure.

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Authors and Affiliations

  1. Spinoza Institute, Utrecht University, Leuvenlaan 4, 3584 CE, Utrecht

    Ruben Costa-Santos

  2. C.N. Yang Institute for Theoretical Physics, State University of New York at, Stony Brook, New York, 11794-3840

    Barry M. McCoy

Authors
  1. Ruben Costa-Santos
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  2. Barry M. McCoy
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Costa-Santos, R., McCoy, B.M. Finite Size Corrections for the Ising Model on Higher Genus Triangular Lattices. Journal of Statistical Physics 112, 889–920 (2003). https://doi.org/10.1023/A:1024697307618

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  • DOI: https://doi.org/10.1023/A:1024697307618

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