Pith Number

pith:WQZUFBPI

pith:2026:WQZUFBPIXJXY64XGGKHF47GWUB

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Pad\'e Approximation and Partition Function Zeros

R. G. M. Rodrigues

Padé approximation reduces the number of zeros needed to locate critical temperatures from partition functions without loss of accuracy.

arxiv:2601.12018 v2 · 2026-01-17 · physics.comp-ph

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Claims

C1strongest claim

Applications to the two-dimensional Ising and XY models demonstrate substantial decreases in polynomial degree and computation time while preserving accurate estimates of the critical temperature.

C2weakest assumption

The Padé approximation preserves the location of the relevant zeros (and thus the critical temperature) without introducing systematic bias, especially in the XY model where convergence issues previously appeared.

C3one line summary

Padé approximation reduces the polynomial degree and computation time for accurate critical temperature estimates from Fisher zeros in 2D Ising and XY models.

References

30 extracted · 30 resolved · 0 Pith anchors

[1] C. N. Yang, T. D. Lee, Statistical theory of equations of state and phase transitions. i. theory of condensation, Phys. Rev. 87 (1952) 404–409. doi:10.1103/PhysRev.87.404. URLhttps://link.aps.org/doi/ 1952 · doi:10.1103/physrev.87.404

[2] T. D. Lee, C. N. Yang, Statistical theory of equations of state and phase transitions. ii. lattice gas and ising model, Phys. Rev. 87 (1952) 410–419. doi:10.1103/PhysRev.87.410. URLhttps://link.aps.or 1952 · doi:10.1103/physrev.87.410

[3] J. C. Rocha, S. Schnabel, D. P. Landau, M. Bachmann, Lead- ing fisher partition function zeros as indicators of structural transitions in macromolecules, Physics Procedia 57 (2014) 94–98, proceedings 2014 · doi:10.1016/j.phpro.2014.08.139

[4] M. Heyl, A. Polkovnikov, S. Kehrein, Dynamical quantum phase transitions in the transverse-field ising model, Phys. Rev. Lett. 110 (2013) 135704.doi:10.1103/PhysRevLett.110.135704. URLhttps://link.aps 2013 · doi:10.1103/physrevlett.110.135704

[5] I. BENA, M. DROZ, A. LIPOWSKI, Statistical mechanics of equilib- 31 rium and nonequilibrium phase transitions: The yang–lee formalism, International Journal of Modern Physics B 19 (29) (2005) 4269–432 2005 · doi:10.1142/s0217979205032759

Receipt and verification

First computed	2026-05-22T01:03:54.180347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4334285e8ba6f8f72e6328e5e7cd6a0462add5c85402719958700bf782e7502

Aliases

arxiv: 2601.12018 · arxiv_version: 2601.12018v2 · doi: 10.48550/arxiv.2601.12018 · pith_short_12: WQZUFBPIXJXY · pith_short_16: WQZUFBPIXJXY64XG · pith_short_8: WQZUFBPI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WQZUFBPIXJXY64XGGKHF47GWUB \
  | 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: b4334285e8ba6f8f72e6328e5e7cd6a0462add5c85402719958700bf782e7502

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.comp-ph",
    "submitted_at": "2026-01-17T11:54:04Z",
    "title_canon_sha256": "cc9cc54d57310ab53c3a69d53674137050891930b122cb19515d2e286a113589"
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