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Journal of Statistical Physics

, Volume 126, Issue 4–5, pp 951–976 | Cite as

Spin Glass Computations and Ruelle’s Probability Cascades

  • Louis-Pierre Arguin
Article

Abstract

We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They are used to derive continuity and monotonicity properties of the functional retrieving a theorem of Guerra. We also detail the connection between the Aizenman-Sims-Starr variational principle and the Parisi formula. As a final application of the techniques, we rederive the Almeida-Thouless line in the spirit of Toninelli but relying on the RPC structure.

Keywords

spin glass Sherrington-Kirkpatrick model Parisi functional GREM 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Louis-Pierre Arguin
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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