{"paper":{"title":"Energy-Weighted Site Percolation in Two Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Bond energy shifts the percolation threshold smoothly and changes the correlation-length exponent continuously in two dimensions.","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Kabir Ramola, Sayan Sircar","submitted_at":"2026-05-18T12:30:51Z","abstract_excerpt":"We study a generalization of two-dimensional site percolation by assigning an energy cost $\\varepsilon$ to bonds between nearest-neighbor occupied sites. This leads to a competition between entropy-driven cluster growth and energetic suppression (or enhancement) of connectivity. Varying $\\varepsilon$ continuously interpolates between dense ferromagnetic-like clusters, ordinary classical percolation, and a dilute regime of minimally connected isolated clusters. Using Monte Carlo simulations and real-space renormalization-group (RG) methods, we show that bond energy shifts the percolation thresh"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Using Monte Carlo simulations and real-space renormalization-group (RG) methods, we show that bond energy shifts the percolation threshold smoothly. We define an energy-weighted correlation length that remains finite at the classical site occupation threshold (p_c(ε=0)) and shrinks with increasing ε, capturing the energetic suppression of large-scale connectivity.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The real-space RG with Kadanoff block recursions accurately tracks the continuous evolution of the correlation-length exponent ν from 1/2 to 4/3 to 1 and matches Coulomb-gas predictions for loop models without requiring additional parameters or post-hoc adjustments specific to the energy term.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Adding a continuous bond energy ε to 2D site percolation shifts the threshold smoothly and drives the correlation-length exponent ν from 1/2 through 4/3 to 1, as shown by Monte Carlo simulations and real-space RG that also reveal an energy-weighted correlation length and antiferromagnetic ordering,","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Bond energy shifts the percolation threshold smoothly and changes the correlation-length exponent continuously in two dimensions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1279c42dd0ac5f664bbef9799d4a97e3f95815f0337beb077339299fc42ff1cd"},"source":{"id":"2605.18312","kind":"arxiv","version":1},"verdict":{"id":"305f7100-a8fd-44ed-aef5-218f825a5f58","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:55:21.666710Z","strongest_claim":"Using Monte Carlo simulations and real-space renormalization-group (RG) methods, we show that bond energy shifts the percolation threshold smoothly. We define an energy-weighted correlation length that remains finite at the classical site occupation threshold (p_c(ε=0)) and shrinks with increasing ε, capturing the energetic suppression of large-scale connectivity.","one_line_summary":"Adding a continuous bond energy ε to 2D site percolation shifts the threshold smoothly and drives the correlation-length exponent ν from 1/2 through 4/3 to 1, as shown by Monte Carlo simulations and real-space RG that also reveal an energy-weighted correlation length and antiferromagnetic ordering,","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The real-space RG with Kadanoff block recursions accurately tracks the continuous evolution of the correlation-length exponent ν from 1/2 to 4/3 to 1 and matches Coulomb-gas predictions for loop models without requiring additional parameters or post-hoc adjustments specific to the energy term.","pith_extraction_headline":"Bond energy shifts the percolation threshold smoothly and changes the correlation-length exponent continuously in two dimensions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18312/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-20T00:02:52.399518Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T00:01:20.476096Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.197702Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T23:21:58.879228Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b23c5e551f0fafdace6d90db6cc6161b85da431b5b7e260b5a5c0b2574caabbf"},"references":{"count":85,"sample":[{"doi":"","year":null,"title":"In the dense cluster limit, asεapproaches−∞, loops become abundant with a loop fugacity ofn= 2","work_id":"531bbfb9-58af-411c-a361-4de6580f4d9b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1994,"title":"D. 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Aharony,Introduction to Percolation Theory(Taylor & Francis, 1994)","work_id":"7ea51201-081f-407b-986b-d540c279bf07","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"Bollob´ as and O","work_id":"4f1bbe07-a097-42e3-a117-5dc17592b066","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1982,"title":"Kesten,Percolation Theory for Mathematicians (Birkh¨ auser, 1982)","work_id":"bd9b64eb-8699-4210-bcb0-71af902ba74e","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1994,"title":"Sahimi,Applications of Percolation Theory(Taylor & Francis, 1994)","work_id":"2eb5df91-a32c-42d3-8ee8-031800a42fb1","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":85,"snapshot_sha256":"cb69b004ba0d983979582f2f0a2664d5ec5925f1cf8978291fb19d21f876ccc0","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5f3bee70bfd959c90f4513cf45f26f48a4269866e0e20cff1847ecf79f838198"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}