Two-dimensional Heisenberg model with nonlinear interactions

Abstract

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