Pith Number

pith:O5HOG5Q2

pith:2026:O5HOG5Q2UH5DJSGHYJ2KBCSCQN

not attested not anchored not stored refs resolved

Landau free energy and the absence of spontaneous magnetization of the one-dimensional Ising model

J. M. Zhang, R. K. Lin, Z. F. Zheng

The one-dimensional Ising model has no spontaneous magnetization at any finite temperature because its Landau free energy is minimized at zero magnetization.

arxiv:2605.06691 v1 · 2026-05-02 · 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{O5HOG5Q2UH5DJSGHYJ2KBCSCQN}

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

We also show that the Landau free energy is an increasing function of |m| and its second derivative at m=0 is positive and non-analytic in temperature, proving rigorously the absence of spontaneous magnetization of the model at any finite temperature.

C2weakest assumption

The maximum-term approximation becomes exact in the thermodynamic limit because the density of states has a simple analytical form that allows the largest term to dominate without significant corrections from other terms.

C3one line summary

The one-dimensional Ising model has no spontaneous magnetization at finite temperatures, proven by showing its Landau free energy increases with magnetization magnitude and has positive second derivative at zero.

References

16 extracted · 16 resolved · 0 Pith anchors

[1] Ising E 1925 Beitrag zur Theorie des Ferromagnetismus Z. Phys. 31 253 1925

[2] An English translation of Ising’s original paper can be found here: https://www.hs-augsburg.de/ ~harsch/anglica/Chronology/20thC/Ising/isi_fm00.html

[3] Peliti L 2011 Statistical Mechanics in a Nutshell (Princeton: Princ eton University Press) 2011

[4] Landau L D and Lifshitz E M 1986 Statistical Physics Part 1 (Singap ore: World Scientiﬁc) 1986

[5] Landau L D 1936 The theory of phase transitions Nature 138 840 1936

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:12.468930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

774ee3761aa1fa34c8c7c274a08a4283731a3c9c904e00e7405ffd5db00b081e

Aliases

arxiv: 2605.06691 · arxiv_version: 2605.06691v1 · doi: 10.48550/arxiv.2605.06691 · pith_short_12: O5HOG5Q2UH5D · pith_short_16: O5HOG5Q2UH5DJSGH · pith_short_8: O5HOG5Q2

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/O5HOG5Q2UH5DJSGHYJ2KBCSCQN \
  | 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: 774ee3761aa1fa34c8c7c274a08a4283731a3c9c904e00e7405ffd5db00b081e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a22f72bc64b85883c3c297322f5bee71eab74eab4e833a59a05a65d23976347",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-02T08:15:00Z",
    "title_canon_sha256": "bc005d770d4a938a1f1567aabb7073a8f5cc90830e5553a76bbaec22a8053055"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06691",
    "kind": "arxiv",
    "version": 1
  }
}