Huse Krauth Moessner Sondhi 2003

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'''Abstract:''' We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the square lattice predicts that the dimers are in a critical Coulomb phase with algebraic, dipolar, correlations, in excellent agreement with our large-scale Monte Carlo simulations. The non-bipartite FCC and Fisher lattices lack such a representation, and we find that these models have both confined and exponentially deconfined but no critical phases. We conjecture that extended critical phases are realized only on bipartite lattices, even in higher dimensions. '''Abstract:''' We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the square lattice predicts that the dimers are in a critical Coulomb phase with algebraic, dipolar, correlations, in excellent agreement with our large-scale Monte Carlo simulations. The non-bipartite FCC and Fisher lattices lack such a representation, and we find that these models have both confined and exponentially deconfined but no critical phases. We conjecture that extended critical phases are realized only on bipartite lattices, even in higher dimensions.
-[http://whttp://arxiv.org/pdf/cond-mat/0305318v3 Electronic version (arXiv)]+[http://arxiv.org/pdf/cond-mat/0305318v3 Electronic version (arXiv)]
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 +[http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.91.167004 Paper in Physical Review Letters (Subscription needed)]
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 +[[image:Dimer_cluster.gif|100px|right|frame|Rejection-free cluster algorithm for dimers developed in [[Krauth Moessner 2003| Roderich Moessner]] and adapted for this paper for the case of three spatial dimensions (not shown). Dimers flip about a symmetry axis between one valid configuration and another.]]

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D. A. Huse, W. Krauth, R. Moessner, S. L. Sondhi Coulomb and Liquid Dimer Models in Three Dimensions Physical Review Letters 91 167004 (2003)

Abstract: We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the square lattice predicts that the dimers are in a critical Coulomb phase with algebraic, dipolar, correlations, in excellent agreement with our large-scale Monte Carlo simulations. The non-bipartite FCC and Fisher lattices lack such a representation, and we find that these models have both confined and exponentially deconfined but no critical phases. We conjecture that extended critical phases are realized only on bipartite lattices, even in higher dimensions.

Electronic version (arXiv)

Paper in Physical Review Letters (Subscription needed)

Rejection-free cluster algorithm for dimers  developed in  Roderich Moessner and adapted for this paper for the case of three spatial dimensions (not shown). Dimers flip about a symmetry axis between one valid configuration and another.
Rejection-free cluster algorithm for dimers developed in Roderich Moessner and adapted for this paper for the case of three spatial dimensions (not shown). Dimers flip about a symmetry axis between one valid configuration and another.
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