Spin Glass Computations and Ruelle's Probability Cascades

Details Spin Glass Computations and Ruelle's Probability Cascades Spin Glass Computations and Ruelle's Probability Cascades

2006-08-17

arxiv.org/abs/math-ph/0608045v1

J. Stat. Phys. Vol.126 (2007) pp.951-976

Physics

Mathematical Physics

20 pages

Scientific paper

10.1007/s10955-006-9207-7

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.

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