Advertisement

Communications in Mathematical Physics

, Volume 76, Issue 2, pp 149–163 | Cite as

Wall and boundary free energies

III. Correlation decay and vector spin systems
  • Gunduz Caginalp
Article
  • 43 Downloads

Abstract

The asymptotic free energy of planar walls and boundaries is analyzed for scalar and vector spin systems. Under the hypothesis of correlation decay, various alternative definitions are found to be equivalent in the thermodynamic limit and independent of the “associated” walls. Furthermore, a torus, or box having periodic boundary conditions, is shown to have no boundary or surface free energy. For vector spin systems withn-component spins, existence of the thermodynamic limit is shown forn=2 and “positive” interactions.

Keywords

Boundary Condition Neural Network Free Energy Statistical Physic Complex System 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fisher, M.E., Caginalp, G.: Commun. Math. Phys.56, 11–56 (1977)Google Scholar
  2. 2.
    Caginalp, G., Fisher, M.E.: Commun. Math. Phys.65, 247–280 (1979)Google Scholar
  3. 3.
    Caginalp, G.: Ph.D. Thesis, Cornell University (1978)Google Scholar
  4. 4.
    Ginibre, J.: Commun. Math. Phys.16, 310–328 (1970); Fortuin, C.M., Kasteleyn, P.W., Ginibre, J.: Commun. Math. Phys.22, 89–102 (1971)Google Scholar
  5. 5.
    Lebowitz, J.L., Penrose, O.: Commun. Math. Phys.11, 99–124 (1968; Phys. Rev. Letters31, 749–752 (1973); Penrose, O., Lebowitz, J.L.: Commun. Math. Phys.39, 165–184 (1974)Google Scholar
  6. 6.
    Gallavotti, G., Miracle-Sole, S.: Commun. Math. Phys.12, 269–274 (1969); Heilmann, O.J., Lieb, E.H.: Commun. Math. Phys.25, 190–232 (1972); Ruelle, D.: Phys. Rev. Lett.26, 303–304 (1971)Google Scholar
  7. 7.
    Iagolnitzer, D., Soulliard, B.: Phys. Rev. A16, 1700–1704 (1977) See also Gross, L.: Commun. Math. Phys.68, 9–27 (1979), and references contained withinGoogle Scholar
  8. 8.
    Lebowitz, J.L.: Commun. Math. Phys.28, 313–321 (1972)Google Scholar
  9. 9.
    Kunz, H., Pfister, C.E., Vuillermot, P.A.: J. Phys. A9, 1673–1683 (1976)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Gunduz Caginalp
    • 1
  1. 1.The Rockefeller UniversityNew YorkUSA

Personalised recommendations