Phase Transition in a Two-Dimensional Heisenberg Model

Abstract

We investigate the two-dimensional classical Heisenberg model with a nonlinear nearest-neighbor interaction $V(\overrightarrow{s},{\overrightarrow{s}}^{\prime })=2K\left[\right(1+\overrightarrow{s}̇{\overrightarrow{s}}^{\prime })/2\mathrm{}{]}^p$. The analogous nonlinear interaction for the $\mathrm{XY}$ 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 $(p=1\mathrm{})$ 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.