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Mean field bipartite spin models treated with mechanical techniques

  • Adriano Barra
  • Andrea Galluzzi
  • Francesco Guerra
  • Andrea Pizzoferrato
  • Daniele Tantari
Regular Article

Abstract

Inspired by a continuously increasing interest in modeling and framing complex systems in a thermodynamic rationale, in this paper we continue our investigation in adapting well-known techniques (originally stemmed in fields of physics and mathematics far from the present) for solving for the free energy of mean field spin models in a statistical mechanics scenario. Focusing on the test cases of bipartite spin systems embedded with all the possible interactions (self and reciprocal), we show that both the fully interacting bipartite ferromagnet, as well as the spin glass counterpart, at least at the replica symmetric level, can be solved via the fundamental theorem of calculus, trough an analogy with the Hamilton-Jacobi theory and lastly with a mapping to a Fourier diffusion problem. All these technologies are shown symmetrically for ferromagnets and spin-glasses in full details and contribute as powerful tools in the investigation of complex systems.

Keywords

Statistical and Nonlinear Physics 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Adriano Barra
    • 1
  • Andrea Galluzzi
    • 2
  • Francesco Guerra
    • 3
  • Andrea Pizzoferrato
    • 4
  • Daniele Tantari
    • 2
  1. 1.Sapienza Università di Roma, Dipartimento di Fisica and GNFM Gruppo di RomaRomeItaly
  2. 2.Sapienza Università di Roma, Dipartimento di Matematica and GNFM Gruppo di RomaRomeItaly
  3. 3.Sapienza Università di Roma, Dipartimento di Fisica and INFN Sezione di RomaRomeItaly
  4. 4.The University of Warwick, Mathematics InstituteCoventryUK

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