Communications in Mathematical Physics

, Volume 90, Issue 2, pp 293–315 | Cite as

Surface models with nonlocal potentials: Upper bounds

  • C. Eugene Wayne


The behavior of fluctuations in a class of surface models with exponentially decaying nonlocal potentials in studied. Combining a Mayer expansion with a duality transformation, we demonstrate the equivalence of these models to a class of two dimensional spin systems with nonlocal interactions. The expansions give sufficient control over the potentials to allow the fluctuations to be bounded from above by the means of complex translations in the spin representation of the model.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Surface Model 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • C. Eugene Wayne
    • 1
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA

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