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 oil triangular-lattice Heisenberg antiferromagnets are discussed.