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Alternative Variational Approach to Cactus Lattices

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Abstract

In this paper, I will present an alternative approach to the Bethe or cactus lattice approximation, widely employed in the theory of cooperative phenomena. This approach relies on a variational free energy, which is equivalent to the Bethe free energy in that it has the same stationary points, but allows one to simplify analytical calculations, since it is a function of only single-site probability distributions, in the same way as an ordinary mean-field (Bragg-Williams) free energy. As an application, I shall discuss a derivation of closed-form equations for critical points in Ising-like models. Moreover, I will suggest a rule of thumb to choose the cactus lattice connectivity yielding the best approximation for the corresponding model defined on an ordinary lattice.

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Authors and Affiliations

  1. Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129, Torino, Italy

    M. Pretti

  2. Center for Statistical Mechanics and Complexity, CNR-INFM Roma 1, Piazzale Aldo Moro 2, I-00185, Roma, Italy

    M. Pretti

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  1. M. Pretti
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Correspondence to M. Pretti.

Additional information

PACS Numbers: 05.20.-y, 05.50.+q, 05.70.Fh, 64.60.-i, 64.60.Cn

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Pretti, M. Alternative Variational Approach to Cactus Lattices. J Stat Phys 127, 1237–1253 (2007). https://doi.org/10.1007/s10955-007-9324-y

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  • DOI: https://doi.org/10.1007/s10955-007-9324-y

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