Finite size corrections for the Ising model on higher genus triangular lattices

Abstract

We study the topology dependence of 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.

final version: 32 pages, tables and eps figures included, typos corrected

References in corpus (4)

• Discrete Riemann Surfaces and the Ising model
• Classical dimers on the triangular lattice
• The Laplacian and $\bar{\partial }$ operators on critical planar graphs
• Dimers and the Critical Ising Model on Lattices of genus>1

Cited by in corpus (7)

• Critical behavior in spherical and hyperbolic spaces
• Universal sub-leading terms in ground state fidelity
• The critical Ising model via Kac-Ward matrices
• Geometric Structures on the Cochains of a Manifold
• Logarithmic corrections to the Ising model free energy on lattices with conical singularities
• The 3D Dimer and Ising Problems Revisited
• Conformal Structures and Period Matrices of Polyhedral Surfaces