Two-dimensional Heisenberg model with nonlinear interactions

We investigate a two-dimensional classical N-vector model with a nonlinear interaction (1+σi⋅σj)p in the large-N limit. As observed for N=3 by Blöte et al. [Phys. Rev. Lett. 88, 047203 (2002)], we find a first-order transition for p>pc and no finite-temperature phase transitions for ppc, both phases have short-range order, the correlation length showing a finite discontinuity at the transition. For p=pc, there is a peculiar transition, where the spin-spin correlation length is finite while the energy-energy correlation length diverges.