Pith Number

pith:WJKK2WJG

pith:2026:WJKK2WJGC7OCGOR3YJYFNB7Q54

not attested not anchored not stored refs pending

Exact solution of a two-dimensional (2D) Ising model with the next nearest interactions

Zhidong Zhang

The exact solution is derived for the two-dimensional Ising model with next-nearest-neighbor interactions at zero magnetic field, yielding closed-form partition function and spontaneous magnetization.

arxiv:2601.10749 v6 · 2026-01-13 · cond-mat.stat-mech

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WJKK2WJGC7OCGOR3YJYFNB7Q54}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The exact solution of a two-dimensional (2D) Ising model with the next nearest interactions at zero magnetic field is derived. The partition function and the spontaneous magnetization are obtained.

C2weakest assumption

That the 2D model with next-nearest interactions is equivalent to a triangular Ising model plus an interaction along the z axis, so that 3D Ising solution methods can be directly modified and applied.

C3one line summary

Exact partition function and spontaneous magnetization obtained for the 2D Ising model with next-nearest interactions via transfer-matrix methods adapted from 3D Ising approaches.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-29T01:05:01.873449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b254ad592617dc233a3bc2705687f0ef22ceb52857f8be38ee767156674d8bf5

Aliases

arxiv: 2601.10749 · arxiv_version: 2601.10749v6 · doi: 10.48550/arxiv.2601.10749 · pith_short_12: WJKK2WJGC7OC · pith_short_16: WJKK2WJGC7OCGOR3 · pith_short_8: WJKK2WJG

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WJKK2WJGC7OCGOR3YJYFNB7Q54 \
  | 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: b254ad592617dc233a3bc2705687f0ef22ceb52857f8be38ee767156674d8bf5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59d8a6be83cc2631a2c717cf3b46c80dd232ee5b18c5c64732276aaee8c4495b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-01-13T00:12:05Z",
    "title_canon_sha256": "d484d97d3ad534ffb1b13aed51e347c3ba6cace61a4733631a167939b17dd46f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.10749",
    "kind": "arxiv",
    "version": 6
  }
}