EXACT FINITE-SIZE RESULTS FOR THE ISING-MODEL ON THE TETRAHEDRON

We propose an approach to statistical systems on lattices with sphere- like topology. Focusing on the Ising model, we consider the thermodyna mic limit along a sequence of lattices with a finite number of defects approaching the large scale geometry of a tetrahedron. The hypothesis of scaling appears to hold at criticality, pointing at a sensible def inition of the continuum limit of the model in the polyhedron. Finite size scaling is shown to produce, however, an anomalous exponent for t he critical behavior of the correlation length, which we determine alt ernatively by looking at the temperature dependence of the gap at larg e lattice size.