Communications in Mathematical Physics

, Volume 65, Issue 3, pp 247–280 | Cite as

Wall and boundary free energies

II. General domains and complete boundaries
  • Gunduz Caginalp
  • Michael E. Fisher


The asymptotic free energy of a planar wall with potentialsW, cut in scalar spin systems, with ferromagnetic interactionsK, enclosed in general domains subject to reasonable shape conditions, is shown (under conditions used in Part I) to exist and to be equal to the unique limiting wall free energy,fx(K,W), of simple rectangular or box domains. Similar results are found for sets of walls forming the complete boundaries of domains; for “subfree” walls bulk plus a uniquely-defined surface term. Some limited results for periodic boundary conditions are reported.


Neural Network Free Energy Nonlinear Dynamics Periodic Boundary Periodic Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Fisher, M.E., Caginalp, G.: Commun. math. Phys.56, 11–56 (1977)Google Scholar
  2. 2.
    Fisher, M.E.: Arch. Rat. Mech. Anal.17, 377–410 (1964)Google Scholar
  3. 3.
    Ruelle, D.: Helv. Phys. Acta36, 183–197 (1963)Google Scholar
  4. 4.
    Griffiths, R.B.: J. Math. Phys.8, 478–489 (1967)Google Scholar
  5. 5.
    Kelly, D.G., Sherman, S.: J. Math. Phys.9, 466–484 (1968)Google Scholar
  6. 6.
    Caginalp, G.: Ph. D. Thesis, Cornell University (1978)Google Scholar
  7. 7.
    Ruelle, D.: Statistical mechanics — rigorous results. New York: Benjamin 1969Google Scholar
  8. 8.
    Gallavotti, G., Miracle-Solé, S.: Commun. math. Phys.5, 317–323 (1967)Google Scholar
  9. 9.
    Fisher, M.E., Lebowitz, J.L.: Commun. math. Phys.19, 251–272 (1970)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Gunduz Caginalp
    • 1
  • Michael E. Fisher
    • 1
  1. 1.Baker LaboratoryCornell UniversityIthacaUSA

Personalised recommendations