2006/08/17 by Louis-Pierre Arguin, Louis‐Pierre Arguin
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algorithm #Complex Systems and Time Series Analysis #Computation #Connection (principal bundle) #Mathematical analysis #Mathematical physics #Mathematics #Monotonic function #Physics #Probability theory #Quantum mechanics #Spin glass #Statistical Mechanics and Entropy #Statistical physics #Topological and Geometric Data Analysis #cond-mat.dis-nn #math-ph #math.MP #msc:60K35 #msc:82B44
paper · pdf · doi:10.1007/s10955-006-9207-7
published as J. Stat. Phys. Vol.126 (2007) pp.951-976 · 20 pages
arxiv created 2006/08/17 · openalex publication_date 2006/11/29 · arxiv updated 2010/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.