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.
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Arguin, LP. Spin Glass Computations and Ruelle’s Probability Cascades. J Stat Phys 126, 951–976 (2007). https://doi.org/10.1007/s10955-006-9207-7
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DOI: https://doi.org/10.1007/s10955-006-9207-7