Two-dimensional Heisenberg model with nonlinear interactions: 1/N corrections

We investigate a two-dimensional classical N-vector model with a generic nearest-neighbor interaction W( sigma i middot sigma 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/N32/ 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= infinity.