Exact free energy functionals for non-simply-connected lattices

J. K. Percus, L. Šamaj

Research output: Contribution to journalArticlepeer-review


We consider the nearest-neighbor Ising model in thermal equilibrium on a network with no required regularity or symmetry properties. Both coupling strengths and external fields are site-dependent. The objective is to describe this system in terms of a free energy magnetization functional whose conjugate variables are the external fields. For simply connected networks, this inverse problem has a local structure. On generalizing to loops, the local structure remains if the description is expanded in an overcomplete fashion to include a collective amplitude with respect to which the free energy is stationary. For more complex connectivity, a superbond representation is developed in terms of which the system can be described by a combined auxiliary set of branch and node collective variables.

Original languageEnglish (US)
Pages (from-to)421-440
Number of pages20
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Oct 1994


  • Inhomogeneous Ising model
  • collective modes
  • free-energy functional

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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