Spin Glass Computations and Ruelle's Probability Cascades
Mathematical Physics
2010-11-09 v1 Disordered Systems and Neural Networks
math.MP
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.
Cite
@article{arxiv.math-ph/0608045,
title = {Spin Glass Computations and Ruelle's Probability Cascades},
author = {Louis-Pierre Arguin},
journal= {arXiv preprint arXiv:math-ph/0608045},
year = {2010}
}
Comments
20 pages