  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 $N=\infty$
