Phase transition in a two-dimensional Heisenberg model.

We investigate the two-dimensional classical Heisenberg model with a nonlinear nearest-neighbor interaction V(s,s') = 2K[(1+s x s')/2]p. The analogous nonlinear interaction for the XY model was introduced by Domany, Schick, and Swendsen, who find that for large p the Kosterlitz-Thouless transition is preempted by a first-order transition. Here we show that, whereas the standard (p = 1) Heisenberg model has no phase transition, for large enough p a first-order transition appears. Both phases have only short-range order, but with a correlation length that jumps at the transition.