{"paper":{"title":"A phase transition for the two-dimensional random field Ising/FK-Ising model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Aoteng Xia, Chenxu Hao, Fenglin Huang","submitted_at":"2025-03-20T15:59:49Z","abstract_excerpt":"We study the total variation (TV) distance between the laws of the 2D Ising/FK-Ising model in a box of side-length $N$ with and without an i.i.d.\\ Gaussian external field with variance $\\epsilon^2$. Letting the external field strength $\\epsilon = \\epsilon(N)$ depend on the size of the box, we derive a phase transition for each model depending on the order of $\\epsilon(N)$. For the random field Ising model, the critical order for $\\epsilon$ is $N^{-1}$. For the random field FK-Ising model, the critical order depends on the temperature regime: for $T>T_c$, $T=T_c$ and $T\\in (0, T_c)$ the critica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16268","kind":"arxiv","version":2},"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/2503.16268/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"}