Is there a phase transition in the isotropic Heisenberg anti-ferromagnet on the triangular lattice?

Abstract

The phase diagram of the classical anisotropic (XXZ) Heisenberg model on the two-dimensional triangular lattice is investigated using Monte Carlo methods. In the easy-axis limit, two finite-temperature vortex-unbinding transitions have been observed. In the easy-plane limit, there also appear to be two distinct finite-temperature phase transitions that are very close in temperature. The upper transition corresponds to an Ising-like chirality ordering and the lower temperature transition corresponds to a Kosterlitz-Thouless vortex-unbinding transition. These phase-transition lines all meet at the Heisenberg point and provide strong evidence that the isotropic model undergoes a novel finite-temperature phase transition.