Ising transition driven by frustration in a 2D classical model with SU(2) symmetry

C. Weber; L. Capriotti; G. Misguich; F. Becca; M. Elhajal; F. Mila

doi:10.1103/PhysRevLett.91.177202

paper

Ising transition driven by frustration in a 2D classical model with SU(2) symmetry

arXiv:cond-mat/0307431 · doi:10.1103/PhysRevLett.91.177202

Abstract

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 {\it finite-temperature} phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that $T_{c} \to 0$ with an infinite slope when $J_{2} / J_{1} \to 1/2$ .

4 pages with 4 figures