Meron-Cluster Simulation of the $\theta$ Vacuum in the 2D O(3) Model

The 2D O(3) model with a $\theta$ vacuum term is formulated in terms of Wolff clusters. Each cluster carries an integer or half-integer topological charge. The clusters with charge ±½ are identified as merons. At $\theta =\pi$ the merons are bound in pairs inducing a second order phase transition at which the mass gap vanishes. The construction of an improved estimator for the topological charge distribution makes numerical simulations of the phase transition feasible. The measured critical exponents agree with those of the $k=1\mathrm{}$ Wess-Zumino-Novikov-Witten (WZNW) model. Our results are consistent with Haldane's conjecture fro 1D antiferromagnetic quantum spin chains.