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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.2154","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2013-09-09T13:36:43Z","cross_cats_sorted":[],"title_canon_sha256":"b88c76e62decf94e6735f6960da0aabbcbee39ae56b4c29039d7db028dc2c42f","abstract_canon_sha256":"7ae9e3c221e3fe23c464110661050c7cebf6059b05e064934390c5aade224214"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:20.536088Z","signature_b64":"xMJR94ZgNksXA7F0HEoBxu15wlsllYF0AD9Sga/rC9SBRKkIu8iz7s209QJxC4fbAWZZrxdNBsT6QUO+6yiLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"928f1cb4edd08ca9ca780367bedc9ae5cc7258ac1052609e0798b66a6f20cd10","last_reissued_at":"2026-05-18T03:02:20.535309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:20.535309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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