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

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

1995-05-24

arxiv.org/abs/hep-lat/9505019v1

Phys.Rev.Lett.75:4524-4527,1995

Physics

High Energy Physics

High Energy Physics - Lattice

8 pages, gzip'ed uuencoded postscript file, 3 figures included

Scientific paper

10.1103/PhysRevLett.75.4524

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.

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