Pith Number

pith:K3F5ATVG

pith:2025:K3F5ATVGZA47BKZCTMSM4BLXPG

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Survey on Lattice Gas Models on 2D Lattices: Critical Behavior of Closed Trajectories

Tianyi Zhou

In two-dimensional Lorentz lattice gases, closed trajectories at special scatterer concentrations show scale-free statistics and fractal geometry with exponents matching percolation hulls.

arxiv:2512.23129 v3 · 2025-12-29 · cond-mat.stat-mech

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Claims

C1strongest 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.

C2weakest assumption

The scaling hypothesis for loop-length distributions holds and connects directly to percolation-hull scaling without additional fitting parameters or post-hoc adjustments.

C3one 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.

References

24 extracted · 24 resolved · 2 Pith anchors

[1] Th. W. Ruijgrok and E. G. D. Cohen,Deterministic lattice gas models, Phys. Lett. A133 (1988), 415–418 1988

[2] 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 1984

[3] X. P. Kong and E. G. D. Cohen,Anomalous diffusion in Lorentz lattice gases, Phys. Rev. B40 (1989), 4838–4845 1989

[4] R. M. Ziff,Test of scaling exponents for percolation-cluster perimeters, Phys. Rev. Lett.56 (1986), 545–548 1986

[5] H. Saleur and B. Duplantier,Exact determination of the percolation hull exponent in two dimensions, Phys. Rev. Lett.58(1987), 2325–2328 1987

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Receipt and verification

First computed	2026-05-18T03:09:32.380679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56cbd04ea6c839f0ab229b24ce0577798a000130ab45bd354c30374eda9d741d

Aliases

arxiv: 2512.23129 · arxiv_version: 2512.23129v3 · doi: 10.48550/arxiv.2512.23129 · pith_short_12: K3F5ATVGZA47 · pith_short_16: K3F5ATVGZA47BKZC · pith_short_8: K3F5ATVG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/K3F5ATVGZA47BKZCTMSM4BLXPG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 56cbd04ea6c839f0ab229b24ce0577798a000130ab45bd354c30374eda9d741d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c138fd0d517edc45f86266370376d88934ba49f48574e97b30e884c01c61ae9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2025-12-29T01:11:42Z",
    "title_canon_sha256": "0fa07edb26f42d2a47bef453c51d5c37130f73631dd65ae77842b9ae7b04142a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.23129",
    "kind": "arxiv",
    "version": 3
  }
}