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Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q

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2013-01
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American Physical Society
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We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of q. This unexpected result is proven rigorously by using a Peierls argument to measure the entropic advantage of sublattice long-range order. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.
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Square-lattice, Monte-Carlo, Zero-temperature, Models, Representation, Spin
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Huang, Y., Chen, K., Deng, Y., Jacobsen, J. L., Kotecký, R., Salas, J., Sokal, A. D. & Swart, J. M. (2013). Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q. Physical Review E, 87(1), 012136.