{"paper":{"title":"The two-particle-irreducible vertex of the two-dimensional lattice $\\phi^4$ model across the Ising transition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-lat","physics.comp-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Lode Pollet","submitted_at":"2026-08-05T06:34:04Z","abstract_excerpt":"We reconstruct the 2PI vertex $\\Gamma(k,p;q)$ from Monte Carlo measurements of the connected two-particle correlator for the two-dimensional single-component $\\phi^4$ lattice field theory and follow it across the Ising transition. Resolving the vertex in the irreducible representations of the point group $C_{4v}$, we find that the instability is driven by the $A_1$ (ferromagnetic) channel at zero transfer, whose leading eigenvalue of the symmetrized Bethe--Salpeter kernel approaches unity. Substantial $B_1$ (nematic) and $B_2$ (diagonal nematic) contributions cooperate with $A_1$ across all sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04497","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/2608.04497/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"}