{"paper":{"title":"Phase Transitions in the semi-infinite Ising model with a decaying field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Jo\\~ao Maia, Rodrigo Bissacot","submitted_at":"2023-11-29T20:09:25Z","abstract_excerpt":"We study the semi-infinite Ising model with an external field $h_i = \\lambda |i_d|^{-\\delta}$, $\\lambda$ is the wall influence, and $\\delta>0$. This external field decays as it gets further away from the wall. We are able to show that when $\\delta>1$ and $\\beta > \\beta_c(d)$, there exists a critical value $0< \\lambda_c:=\\lambda_c(\\delta,\\beta)$ such that, for $\\lambda<\\lambda_c$ there is phase transition and for $\\lambda>\\lambda_c$ we have uniqueness of the Gibbs state. In addition, when $\\delta<1$, we have only one Gibbs state for any positive $\\beta$ and $\\lambda$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.18058","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.18058/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}