Mean field bipartite spin models treated with mechanical techniques

Adriano Barra, Andrea Galluzzi (), Francesco Guerra, Andrea Pizzoferrato and Daniele Tantari

The European Physical Journal B: Condensed Matter and Complex Systems, 2014, vol. 87, issue 3, 1-13

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. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Keywords: Statistical and Nonlinear Physics (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1140/epjb/e2014-40952-4 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:87:y:2014:i:3:p:1-13:10.1140/epjb/e2014-40952-4

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/e2014-40952-4

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().