{"paper":{"title":"Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin-glass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Cecile Monthus, Thomas Garel","submitted_at":"2013-09-09T13:36:43Z","abstract_excerpt":"The long-range one-dimensional Ising spin-glass with random couplings decaying as $J(r) \\propto r^{-\\sigma}$ presents a spin-glass phase $T_c(\\sigma)>0$ for $0 \\leq \\sigma<1$ (the limit $\\sigma=0$ corresponds to the mean-field SK-model). We use the eigenvalue method introduced in our previous work [C. Monthus and T. Garel, J. Stat. Mech. P12017 (2009)] to measure the equilibrium time $t_{eq}(N)$ at temperature $T=T_c(\\sigma)/2$ as a function of the number $N$ of spins. We find the activated scaling $\\ln t_{eq}(N) \\sim N^{\\psi}$ with the same barrier exponent $\\psi \\simeq 0.33$ in the whole reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2154","kind":"arxiv","version":3},"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"}