Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-10-02
J.Statist.Phys. 112 (2003) 889-920
Physics
Condensed Matter
Statistical Mechanics
final version: 32 pages, tables and eps figures included, typos corrected
Scientific paper
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.
Costa-Santos Ruben
McCoy Barry M.
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