{"paper":{"title":"Analysis of quantities determining the critical inverse temperature in the annealed Potts model with Pareto vertex weights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"A.J.E.M. Janssen","submitted_at":"2025-08-29T08:32:04Z","abstract_excerpt":"We consider in this work the crucial quantity $t_c$ that determines the critical inverse temperature $\\beta_c$ in the $q$-state Potts model on sparse rank-1 random graphs where the vertices are equipped with a Pareto weight density $(\\tau-1)\\,w^{-\\tau}\\,{\\cal X}_{[1,\\infty)}(w)$. It is shown in \\cite{ref1} that this $t_c$ is the unique positive zero of a function ${\\cal K}$ that is obtained by an appropriate combination of the stationarity condition and the criticality condition for the case the external field $B$ equals 0 and that $q\\geq3$ and $\\tau\\geq4$, see \\cite{ref1}, Theorem~1.14 and Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.21409","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.21409/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"}