Exact Finite Size Results on the Ising Model in 2D Curved Space

Abstract

We propose an approach to statistical systems on lattices with sphere-like topology. Focusing on the Ising model, we consider the thermodynamic limit along a sequence of lattices which preserve the {\em fixed} large scale geometry. The hypothesis of scaling appears to hold at criticality, pointing at a sensible definition of the continuum limit of the model in the curved space.

18 pages (uses LaTeX and epsf), 6 figures included (4 in postscript files encoded through uufiles), PUPT-1367