Evan Owen, BU: Lattice simulation of the critical Ising model on a 2-sphere

We derive the critical values of coupling constants for an Ising model defined on a general 2-dimensional simplicial lattice in terms of edge lengths. Applying these coupling constants to a discretization of a 2-sphere and performing Monte Carlo simulations, we show that full O(3) symmetry of correlation functions is recovered in the continuum limit only for lattice discretizations with smoothly varying triangular cells and uniform effective lattice spacing. Finally, we show that CFT data extracted from simulations on such lattices is consistent with the 2d Ising CFT.