{"paper":{"title":"Survey on Lattice Gas Models on 2D Lattices: Critical Behavior of Closed Trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"In two-dimensional Lorentz lattice gases, closed trajectories at special scatterer concentrations show scale-free statistics and fractal geometry with exponents matching percolation hulls.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Tianyi Zhou","submitted_at":"2025-12-29T01:11:42Z","abstract_excerpt":"Lorentz lattice gases (LLGs) are discrete-time transport models in which a point particle moves ballistically between lattice sites and is scattered by randomly placed, quenched local scatterers such as ``rotators'' or ``mirrors.'' Despite the elementary update rules, LLGs exhibit rich dynamical regimes: typically, trajectories close quickly and the distribution of loop lengths has exponential tails, but at special concentrations of scatterers one observes critical behavior with scale-free statistics and fractal geometry. This survey focuses on the critical behavior of closed trajectories in t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"At special concentrations of scatterers one observes critical behavior with scale-free statistics and fractal geometry, with exponents τ=15/7, d_f=7/4, and σ=3/7 in several universality classes.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The scaling hypothesis for loop-length distributions holds and connects directly to percolation-hull scaling without additional fitting parameters or post-hoc adjustments.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The survey summarizes critical exponents τ=15/7, d_f=7/4, and σ=3/7 for closed trajectories in 2D Lorentz lattice gases across several universality classes, linking them to percolation-hull scaling.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In two-dimensional Lorentz lattice gases, closed trajectories at special scatterer concentrations show scale-free statistics and fractal geometry with exponents matching percolation hulls.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cd1ef17b9da4c78c00ce6509b38e179c76b65fd9dde2867ed38ab41923a18708"},"source":{"id":"2512.23129","kind":"arxiv","version":3},"verdict":{"id":"61c29b05-f10b-430e-97a5-a6855a4d0139","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T20:03:57.420671Z","strongest_claim":"At special concentrations of scatterers one observes critical behavior with scale-free statistics and fractal geometry, with exponents τ=15/7, d_f=7/4, and σ=3/7 in several universality classes.","one_line_summary":"The survey summarizes critical exponents τ=15/7, d_f=7/4, and σ=3/7 for closed trajectories in 2D Lorentz lattice gases across several universality classes, linking them to percolation-hull scaling.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The scaling hypothesis for loop-length distributions holds and connects directly to percolation-hull scaling without additional fitting parameters or post-hoc adjustments.","pith_extraction_headline":"In two-dimensional Lorentz lattice gases, closed trajectories at special scatterer concentrations show scale-free statistics and fractal geometry with exponents matching percolation hulls."},"references":{"count":24,"sample":[{"doi":"","year":1988,"title":"Th. W. Ruijgrok and E. G. D. Cohen,Deterministic lattice gas models, Phys. Lett. A133 (1988), 415–418","work_id":"5cc7b871-be71-4722-9d6c-da32dd00ae53","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1984,"title":"R. M. Ziff, P. T. Cummings, and G. Stell,Generation of percolation cluster perimeters by a random walk, J. Phys. A: Math. Gen.17(1984), 3009–3017","work_id":"fa61a698-4041-49e9-b1f7-9a6cb6beba34","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1989,"title":"X. P. Kong and E. G. D. Cohen,Anomalous diffusion in Lorentz lattice gases, Phys. Rev. B40 (1989), 4838–4845","work_id":"74986fbb-e745-4f23-8a2a-82ac5d26e3b9","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1986,"title":"R. M. Ziff,Test of scaling exponents for percolation-cluster perimeters, Phys. Rev. Lett.56 (1986), 545–548","work_id":"35ab7a59-a0fe-42fb-8207-647eedf78857","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1987,"title":"H. Saleur and B. Duplantier,Exact determination of the percolation hull exponent in two dimensions, Phys. Rev. Lett.58(1987), 2325–2328","work_id":"a9d39c55-90a2-49c5-be67-0e484e0da8c5","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":24,"snapshot_sha256":"b4dcab08977ba53d0d12c6d4d810cf879b3558a450bba1bd5d0c62b8487cbc2a","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a3870a50ddfbbda8e9bed1fc01c8d5d1449f79ffffd666b48291a78e7260c732"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}