{"paper":{"title":"Critical quench dynamics of Wegner's $\\mathbb{Z}_2$ gauge model: a geometric perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"In Wegner's Z2 gauge model the percolation order parameter relaxes at criticality with dynamical exponent z_p approximately 2.6, the same value found for the energy density.","cross_cats":["hep-lat","hep-th"],"primary_cat":"cond-mat.stat-mech","authors_text":"Leticia F. Cugliandolo, Marco Picco, Ramgopal Agrawal","submitted_at":"2026-05-15T10:54:56Z","abstract_excerpt":"Wegner's $\\mathbb{Z}_2$ gauge model is the earliest formulation of pure lattice gauge theory and predicts the topological nature of the confinement-deconfinement transition. In three dimensions ($D=3$), the equilibrium critical behavior of the model is understood in terms of geometrically defined objects, namely loop excitations and Fortuin-Kasteleyn (FK) clusters. This work investigates the critical quench dynamics of this model from a geometric perspective, following quenches from both a high-temperature percolation phase and the zero-temperature ground state. Using time-dependent finite-siz"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The critical non-equilibrium relaxation of the percolation order parameter is governed by a dynamical exponent z_p ≃ 2.6, consistent with that associated with the energy density, z_c. Importantly, the value of z_p is robust with respect to the initial quench condition and the choice of geometrical objects.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That time-dependent finite-size scaling can be reliably applied to the percolation order parameter and geometric observables in this model, even in the absence of a local order parameter and without detailed knowledge of finite-size corrections or equilibration criteria.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quench dynamics of the 3D Z2 gauge model yield a dynamical exponent z_p ≈ 2.6 for the percolation order parameter that matches the energy-density exponent and remains robust across initial conditions and geometric observables.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In Wegner's Z2 gauge model the percolation order parameter relaxes at criticality with dynamical exponent z_p approximately 2.6, the same value found for the energy density.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ecb4415c9657b98d7ec1f374fba1c91c17330afa6911516f5601cb349d25bd6c"},"source":{"id":"2605.15841","kind":"arxiv","version":1},"verdict":{"id":"109c0d2a-aa57-4493-bd7c-44184cc2d9c4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:23:38.518554Z","strongest_claim":"The critical non-equilibrium relaxation of the percolation order parameter is governed by a dynamical exponent z_p ≃ 2.6, consistent with that associated with the energy density, z_c. Importantly, the value of z_p is robust with respect to the initial quench condition and the choice of geometrical objects.","one_line_summary":"Quench dynamics of the 3D Z2 gauge model yield a dynamical exponent z_p ≈ 2.6 for the percolation order parameter that matches the energy-density exponent and remains robust across initial conditions and geometric observables.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That time-dependent finite-size scaling can be reliably applied to the percolation order parameter and geometric observables in this model, even in the absence of a local order parameter and without detailed knowledge of finite-size corrections or equilibration criteria.","pith_extraction_headline":"In Wegner's Z2 gauge model the percolation order parameter relaxes at criticality with dynamical exponent z_p approximately 2.6, the same value found for the energy density."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15841/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.085813Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:31:11.914014Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.713680Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.843299Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1aacb41fad030fda328d082b5543a574201dda024f638b0866c9b46c57c1460f"},"references":{"count":65,"sample":[{"doi":"","year":null,"title":"The critical relaxation of the percolation order parameter is governed by a dynamical exponentz p ≃2.6, consistent with the corresponding exponent for energy relaxation, zc","work_id":"2bf853d2-841b-4791-8136-c626eeb0a975","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The value ofz p is robust, within error bars, with respect to both the quench protocol and the choice of geometrically defined objects","work_id":"ee05a01a-c2ea-4ff6-a29d-74196cac8724","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The time evolution of the number statisticsN(s, t) of geometrical objects of sizes, following a quench from the percolation phase, supports a dynamic scaling framework governed by a time-dependent len","work_id":"2de2f7bb-ba1f-4432-83bd-770319f77033","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"We structure this paper as follows","work_id":"86df0935-f375-4613-9c30-b09a19274d91","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"At early times, large multiple-spanning objects shrink so that smaller ones can accom- modate","work_id":"c2759168-7166-4dc5-8ab0-43ac182cedcd","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":65,"snapshot_sha256":"5db9fee82d4ff517432c2024cac7dbc0de29835c518f04754da4223a5d109197","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"469057b3c5afdcc74e0c184a5e5be3a20151ceb8402b2e5e790f656f77af3586"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}