{"paper":{"title":"Order by disorder up to arbitrarily high temperature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A class of classical lattice models exhibits long-range checkerboard order at high temperatures through a purely entropic mechanism.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Ravish Mehta","submitted_at":"2026-04-30T15:42:38Z","abstract_excerpt":"We prove that a class of classical lattice models on $\\mathbb{Z}^d$ ($d \\geq 2$) with on-site space $\\mathbb{N}_0$ and nearest neighbour interaction, exhibits long-range checkerboard order at sufficiently high temperature. The ordering mechanism is purely entropic. The class of models contains the recently introduced model of Han--Huang--Komargodski--Lucas--Popov (arXiv:2503.22789), by which our work is inspired. The proof uses Pirogov--Sinai theory and the key input is a Peierls bound."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that a class of classical lattice models on Z^d (d ≥ 2) with on-site space N_0 and nearest neighbour interaction, exhibits long-range checkerboard order at sufficiently high temperature. The ordering mechanism is purely entropic.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The models in the class satisfy the conditions needed for a Peierls bound to hold, which is the key input allowing Pirogov-Sinai theory to establish the high-temperature ordered phase (as stated in the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A class of classical lattice models on Z^d (d≥2) with non-negative integer on-site states and nearest-neighbor interactions exhibits long-range checkerboard order at arbitrarily high temperatures via a purely entropic mechanism, proven using Pirogov-Sinai theory with a Peierls bound.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A class of classical lattice models exhibits long-range checkerboard order at high temperatures through a purely entropic mechanism.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"180ae532d758f8afe66e9116e2b6e85b2ef14b9a7ccd29db5aa36777cf97ff75"},"source":{"id":"2604.28026","kind":"arxiv","version":2},"verdict":{"id":"0e2b3741-85c1-46eb-8781-ac6f4ab33b2a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T16:48:19.950111Z","strongest_claim":"We prove that a class of classical lattice models on Z^d (d ≥ 2) with on-site space N_0 and nearest neighbour interaction, exhibits long-range checkerboard order at sufficiently high temperature. The ordering mechanism is purely entropic.","one_line_summary":"A class of classical lattice models on Z^d (d≥2) with non-negative integer on-site states and nearest-neighbor interactions exhibits long-range checkerboard order at arbitrarily high temperatures via a purely entropic mechanism, proven using Pirogov-Sinai theory with a Peierls bound.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The models in the class satisfy the conditions needed for a Peierls bound to hold, which is the key input allowing Pirogov-Sinai theory to establish the high-temperature ordered phase (as stated in the abstract).","pith_extraction_headline":"A class of classical lattice models exhibits long-range checkerboard order at high temperatures through a purely entropic mechanism."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.28026/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T18:41:30.338531Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b88692005faf5f9ac0e357edc00f5eba23a61b44a441f4eafbe0705d3b06bfa3"},"references":{"count":18,"sample":[{"doi":"","year":2026,"title":"Yiqiu Han, Xiaoyang Huang, Zohar Komargodski, Andrew Lucas, and Fedor K. Popov. Entropic order.Nature Communications, 17:87, 2026","work_id":"f2009d72-18c3-4a44-94a7-a5e06a23740a","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1968,"title":"R. L. Dobrushin. The description of a random field by means of conditional prob- abilities and conditions of its regularity.Theory of Probability & Its Applications, 13(2):197–224, 1968","work_id":"58e67499-50ff-46a8-8ef0-0dd2581d430e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1982,"title":"H. R. Künsch. Decay of correlations under dobrushin’s uniqueness condition and its applications.Communications in Mathematical Physics, 84(2):207–222, 1982","work_id":"3bd334d7-a120-40bc-9cf4-c5b3faa93969","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"De Gruyter, Berlin, 2nd edition, 2011","work_id":"97bdeac5-a3e1-4fb0-b618-a0ff26a30866","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1980,"title":"J. Villain, R. Bidaux, J.-P. Carton, and R. Conte. Order as an effect of disorder. 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