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


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.


Boundary Condition Neural Network Free Energy Statistical Physic Complex System 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

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

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