Phase Transition of the Two-Dimensional Heisenberg Antiferromagnet on the Triangular Lattice

TLDR

The study introduces a vorticity function, analogous to the Wilson loop, to distinguish high‑ and low‑temperature phases and discusses its implications for experimental data on triangular lattice Heisenberg antiferromagnets. The authors investigate the ordering process of the 2D triangular lattice Heisenberg antiferromagnet using topological defect analysis and Monte Carlo simulations, and introduce a vorticity function to probe phase distinctions. The order‑parameter space is isomorphic to SO(3); homotopy analysis reveals a two‑valued topological quantum number and a Kosterlitz‑Thouless‑type transition driven by vortex dissociation, while Monte Carlo results suggest such a transition yet spin correlations decay exponentially even in the low‑temperature phase.

Abstract

Ordering process of the antiferromagnetic Heisenberg model on the two-dimensional triangular lattice is studied both by topological analysis of defects and by Monte Carlo simulation. It is shown that the order parameter space of this model is isomorphic to the three-dimensional rotation group SO(3) due to the inherent frustration effect. Homotopy analysis shows that the system bears a topologically stable point defect characterized by a two-valued topological quantum number and exhibits a phase transition driven by the dissociation of the vortices. A Monte Carlo study on the specific heat and the behavior of vortices strongly suggests the occurence of a Kosterlitz-Thouless-type phase transition. It is, however, argued that in contrast to the two-dimensional X Y model, the spin-correlation function decays exponentially even in the low-temperature phase. In order to distinguish the high- and low-temperature phases qualitatively, we introduce a “vorticity function” analogously to the Wilson loop in the quark-confinement problem in the lattice gauge theory. A discussion is made on possible interpretations of the experimental data for triangular lattice Heisenberg antiferromagnets.