Pith Number

pith:Q4G6LRMF

pith:2026:Q4G6LRMFUEJJBNFCDXMSVSPJES

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Order by disorder up to arbitrarily high temperature

Ravish Mehta

A class of classical lattice models exhibits long-range checkerboard order at high temperatures through a purely entropic mechanism.

arxiv:2604.28026 v2 · 2026-04-30 · cond-mat.stat-mech

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Claims

C1strongest 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.

C2weakest 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).

C3one 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.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] Yiqiu Han, Xiaoyang Huang, Zohar Komargodski, Andrew Lucas, and Fedor K. Popov. Entropic order.Nature Communications, 17:87, 2026 2026

[2] 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 1968

[3] H. R. Künsch. Decay of correlations under dobrushin’s uniqueness condition and its applications.Communications in Mathematical Physics, 84(2):207–222, 1982 1982

[4] De Gruyter, Berlin, 2nd edition, 2011 2011

[5] J. Villain, R. Bidaux, J.-P. Carton, and R. Conte. Order as an effect of disorder. Journal de Physique, 41(11):1263–1272, 1980 1980

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:01:42.331940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

870de5c585a11290b4a21dd92ac9e92496cb2dbab7f83d2d08a3469e1d496795

Aliases

arxiv: 2604.28026 · arxiv_version: 2604.28026v2 · doi: 10.48550/arxiv.2604.28026 · pith_short_12: Q4G6LRMFUEJJ · pith_short_16: Q4G6LRMFUEJJBNFC · pith_short_8: Q4G6LRMF

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q4G6LRMFUEJJBNFCDXMSVSPJES \
  | 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: 870de5c585a11290b4a21dd92ac9e92496cb2dbab7f83d2d08a3469e1d496795

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "159106f3bd3cb60530b6263bae4d609fc92c284a22e895defae510105a1ab22b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-04-30T15:42:38Z",
    "title_canon_sha256": "878e7184558266d46b6594ff48fd1da0bbd13d360b14e79874d71a3d9bf55e80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.28026",
    "kind": "arxiv",
    "version": 2
  }
}