{"paper":{"title":"Critical Exponents of the Random Field Hierarchical Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Giorgio Parisi, Jacopo Rocchi","submitted_at":"2013-09-28T16:04:23Z","abstract_excerpt":"We have studied the one dimensional Dyson hierarchical model in presence of a random field. This is a long range model where the interactions scale with the distance with a power law-like form J(r) ~ r^{-\\rho} and we can explore mean field and non-mean field behavior by changing \\rho. Thus, it can be used to approach the phase transitions in finite-dimensional disordered models. We studied the model at T=0 and we numerically computed its critical exponents in the non-mean field region for Gaussian disorder. We then computed an analytic expression for the critical exponent \\delta, that holds in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7470","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"}