2001/03/19 by Tommaso Rizzo · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1088/0305-4470/34/27/305
published as J. Phys. A: Math. Gen. 34 (2001) 5531-5549 · 20 pages, submitted to J.Phys. A
arxiv created 2001/03/19 · openalex publication_date 2001/06/27 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We study the problem of chaos in temperature in some mean-field spin-glass models by means of a replica computation over a model of coupled systems. We propose a set of solutions of the saddle point equations which are intrinsically non-chaotic and solve a general problem regarding the consistency of their structure. These solutions are relevant in the case of uncoupled systems too. Therefore they imply a non-trivial overlap distribution P ( q T 1 T 2 ) between systems at different temperatures. The existence of such solutions is checked to fifth order in an expansion near the critical temperature through highly non-trivial cancellations, while it is proved that a dangerous set of such cancellations holds exactly at all orders in the Sherrington-Kirkpatrick (SK) model. The SK model with soft-spin distribution is also considered, obtaining analogous results. Previous analytical results are discussed.