Ising transition driven by frustration in a 2D classical model with continuous symmetry

We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest (J(1)) and next-nearest (J(2)) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for J(2)/J(1)>1/2, thermal fluctuations give rise to an effective Z(2) symmetry leading to a finite-temperature phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that T-c-->0 with an infinite slope when J(2)/J(1)-->1/2.