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Magnetization densities as replica parameters: The dilute ferromagnet

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  • Serva, Maurizio

Abstract

In this paper we compute exactly the ground state energy and entropy of the dilute ferromagnetic Ising model. The two thermodynamic quantities are also computed when a magnetic field with random locations is present. The result is reached in the replica approach frame by a class of replica order parameters introduced by Monasson (1998) [5]. The strategy is first illustrated considering the SK model, for which we will show the complete equivalence with the standard replica approach. Then, we apply to the diluted ferromagnetic Ising model with a random located magnetic field, which is mapped into a Potts model.

Suggested Citation

  • Serva, Maurizio, 2010. "Magnetization densities as replica parameters: The dilute ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2700-2707.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:14:p:2700-2707
    DOI: 10.1016/j.physa.2010.03.019
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    References listed on IDEAS

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    1. Barré, Julien & Ciani, Antonia & Fanelli, Duccio & Bagnoli, Franco & Ruffo, Stefano, 2009. "Finite size effects for the Ising model on random graphs with varying dilution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3413-3425.
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    Cited by:

    1. Serva, Maurizio, 2011. "Exact and approximate solutions for the dilute Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2443-2451.
    2. de Almeida, M.L. & Albuquerque, E.L. & Fulco, U.L. & Serva, M., 2014. "A percolation system with extremely long range connections and node dilution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 273-278.

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    1. Serva, Maurizio, 2011. "Exact and approximate solutions for the dilute Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2443-2451.

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