Z₂-vortex ordering of the triangular-lattice Heisenberg antiferromagnet

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.