Exact free energy functionals for non-simply-connected lattices

Jerome Percus, L. Šamaj

Research output: Contribution to journalArticle

Abstract

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
Volume77
Issue number1-2
DOIs
StatePublished - Oct 1994

Fingerprint

Local Structure
functionals
External Field
Free Energy
free energy
Thermal Equilibrium
regularity
Magnetization
Ising model
Ising Model
Nearest Neighbor
Inverse Problem
Connectivity
Branch
Regularity
Symmetry
magnetization
Dependent
symmetry
Vertex of a graph

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Exact free energy functionals for non-simply-connected lattices. / Percus, Jerome; Šamaj, L.

In: Journal of Statistical Physics, Vol. 77, No. 1-2, 10.1994, p. 421-440.

Research output: Contribution to journalArticle

Percus, Jerome ; Šamaj, L. / Exact free energy functionals for non-simply-connected lattices. In: Journal of Statistical Physics. 1994 ; Vol. 77, No. 1-2. pp. 421-440.
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