Z_2-vortex ordering of the triangular-lattice Heisenberg antiferromagnet

TL;DR

This paper investigates the Z_2-vortex driven phase transition in the classical Heisenberg antiferromagnet on a triangular lattice, revealing a topological spin-gel state with finite correlation length and implications for experiments.

Contribution

It demonstrates the role of Z_2-vortex binding-unbinding in the phase transition of the triangular-lattice Heisenberg antiferromagnet using multiple methods.

Findings

Thermodynamic transition driven by Z_2-vortex unbinding

Identification of a topological spin-gel state with finite correlation length

Discussion of experimental implications

Abstract

Ordering of the classical Heisenberg antiferromagnet on the triangular lattice is studied by means of a mean-field calculation, a scaling argument and a Monte Carlo simulation, with special attention to its vortex degree of freedom. The model exhibits a thermodynamic transition driven by the Z_2-vortex binding-unbinding, at which various thermodynamic quantities exhibit an essential singularity. The low-temperature state is a "spin-gel" state with a long but finite spin correlation length where the ergodicity is broken topologically. Implications to recent experiments on triangular-lattice Heisenberg antiferromagnets are discussed.