Journal of Statistical Physics

, Volume 112, Issue 5–6, pp 889–920

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

  • Ruben Costa-Santos
  • Barry M. McCoy
Article

DOI: 10.1023/A:1024697307618

Cite this article as:
Costa-Santos, R. & McCoy, B.M. Journal of Statistical Physics (2003) 112: 889. doi:10.1023/A:1024697307618

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.

Finite size corrections Ising model higher genus theta functions period matrix discrete holomorphy 

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Ruben Costa-Santos
    • 1
  • Barry M. McCoy
    • 2
  1. 1.Spinoza InstituteUtrecht UniversityUtrecht
  2. 2.C.N. Yang Institute for Theoretical PhysicsState University of New York atStony Brook

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