Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections

We investigate a two-dimensional classical $-vector model with a generic nearest-neighbor interaction$W(\bsigma_i\cdot \bsigma_j)$in the large-N limit, focusing on the finite-temperature transition point at which energy-energy correlations become critical. We show that this transition belongs to the Ising universality class. However, the width of the region in which Ising behavior is observed scales as$1/N^{3/2}$along the magnetic direction and as 1/N in the thermal direction; outside a crossover to mean-field behavior occurs. This explains why only mean-field behavior is observed for$N=\infty$