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

Abstract

The 2-d $O(3)$-model with a $\theta$-vacuum term is formulated in terms of Wolff clusters. Each cluster carries a half-integer topological charge. The clusters with charge $\pm 1/2$ 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 $k=1$ Wess-Zumino-Novikov-Witten model. Our results are consistent with Haldane's conjecture for 1-d antiferromagnetic quantum spin chains.

arXiv comment8 pages, gzip'ed uuencoded postscript file, 3 figures included

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• Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain
• Towards a Dynamical Solution of the Strong CP Problem
• On the existence of a first order phase transition at small vacuum angle $\theta$ in the $C{P}^3$ model

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