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Ordering of the classical Heisenberg antiferromagnet on the triangularlattice is studied by means of a mean-field calculation, a scaling argument anda Monte Carlo simulation, with special attention to its vortex degree offreedom. The model exhibits a thermodynamic transition driven by the Z_2-vortexbinding-unbinding, at which various thermodynamic quantities exhibit anessential singularity. The low-temperature state is a "spin-gel" state with along but finite spin correlation length where the ergodicity is brokentopologically. Implications to recent experiments on triangular-latticeHeisenberg antiferromagnets are discussed.

Z_2-vortex ordering of the triangular-lattice Heisenberg antiferromagnet