{"paper":{"title":"A note on the free energy of the coupled system in the Sherrington-Kirkpatrick model","license":"","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"math.PR","authors_text":"Dmitry Panchenko","submitted_at":"2004-05-18T22:12:54Z","abstract_excerpt":"In this paper we consider a system of spins that consists of two configurations $\\vsi^1,\\vsi^2\\in\\Sigma_N=\\{-1,+1\\}^N$ with Gaussian Hamiltonians $H_N^1(\\vsi^1)$ and $H_N^2(\\vsi^2)$ correspondingly, and these configurations are coupled on the set where their overlap is fixed $\\{R_{1,2}=N^{-1}\\sum_{i=1}^N \\sigma_i^1\\sigma_i^2 = u_N\\}.$ We prove the existence of the thermodynamic limit of the free energy of this system given that $\\lim_{N\\to\\infty}u_N = u\\in[-1,1]$ and give the analogue of the Aizenman-Sims-Starr variational principle that describes this limit via random overlap structures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405359","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}