Pith Number

pith:JPW5G57D

pith:2026:JPW5G57DERRXS2KMO3EOJJNCC3

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Mixed response geometry and critical crossover in the Ising model

Eric R. Bittner

Thermodynamic curvature on the temperature-field plane traces the Widom line as a ridge in the Ising model.

arxiv:2604.16707 v3 · 2026-04-17 · cond-mat.stat-mech · cond-mat.dis-nn

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Claims

C1strongest claim

This curvature is given by a mixed derivative of the free energy and can be expressed directly as the covariance between energy and magnetization fluctuations. We evaluate the curvature field using Monte Carlo sampling and demonstrate that it develops a pronounced ridge structure extending from the critical point into the supercritical regime. This identifies the Widom line as a geometric feature of control space.

C2weakest assumption

That the curvature defined via the mixed derivative on the (β, h) manifold remains a faithful and non-redundant descriptor of thermodynamic response once the manifold choice is fixed, and that Monte Carlo sampling on finite lattices accurately locates the ridge without significant finite-size or sampling artifacts.

C3one line summary

Thermodynamic curvature on the (β, h) manifold in the Ising model produces a ridge that geometrically identifies the Widom line as the locus of maximal response extending from the critical point.

Cited by

1 paper in Pith

Mixed response geometry and critical crossover in the Ising model

Receipt and verification

First computed	2026-06-23T02:13:24.030986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bedd377e3246379694c76c8e4a5a216c34a2e952ce8646c77bff56c789a5ae5

Aliases

arxiv: 2604.16707 · arxiv_version: 2604.16707v3 · doi: 10.48550/arxiv.2604.16707 · pith_short_12: JPW5G57DERRX · pith_short_16: JPW5G57DERRXS2KM · pith_short_8: JPW5G57D

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JPW5G57DERRXS2KMO3EOJJNCC3 \
  | 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: 4bedd377e3246379694c76c8e4a5a216c34a2e952ce8646c77bff56c789a5ae5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "411385d839a42a815faa6b08a80be7b45135f224a40c5adc9f0df618137177fd",
    "cross_cats_sorted": [
      "cond-mat.dis-nn"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-04-17T21:18:06Z",
    "title_canon_sha256": "0d666a26f767e9137728b77bb5dfd25f521bd1ba665bed69b245de2c4ffe5ca8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.16707",
    "kind": "arxiv",
    "version": 3
  }
}