Finite Size Corrections for the Ising Model on Higher Genus Triangular Lattices
- Cite this article as:
- Costa-Santos, R. & McCoy, B.M. Journal of Statistical Physics (2003) 112: 889. doi:10.1023/A:1024697307618
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.