{"paper":{"title":"Disorder-dominated phases of random systems : relations between tails exponents and scaling exponents","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Cecile Monthus, Thomas Garel","submitted_at":"2007-10-11T09:50:16Z","abstract_excerpt":"We consider various random models (directed polymer, ferromagnetic random Potts model, Ising spin-glasses) in their disorder-dominated phases, where the free-energy cost $F(L)$ of an excitation of length $L$ present fluctuations that grow as a power-law $\\Delta F(L) \\sim L^{\\omega}$ with the so-called droplet exponent $\\omega>0$. We study the tails of the probability distribution $\\Pi(x)$ of the rescaled free-energy cost $x= \\frac{F_L- \\bar{F_L}}{L^{\\omega}}$, which are governed by two exponents $(\\eta_-,\\eta_+)$ defined by $\\ln \\Pi(x \\to \\pm \\infty) \\sim - | x |^{\\eta_{\\pm}}$. The aim of this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.2198","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"}