Spin Glass Computations and Ruelle’s Probability Cascades |
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Authors: | Louis-Pierre Arguin |
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Institution: | (1) Department of Mathematics, Princeton University, NJ Princeton, 08544, USA |
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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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Keywords: | spin glass Sherrington-Kirkpatrick model Parisi functional GREM |
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