Pith. Sign in

RECORD

Singular Behaviour of the Potts Model in the Thermodynamic Limit

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Ralph Kenna

High Energy Physics - Lattice · Submitted 11 Dec 1997

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This locus, together with the density of zeroes is shown to be sufficient to recover the singular form of all thermodynamic functions in the thermodynamic limit.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDhep-lat/9712013 (version 1)
Pith IDXWS72DUT, Pith's permanent record of this paper and its review
CitationRalph Kenna. "Singular Behaviour of the Potts Model in the Thermodynamic Limit." arXiv:hep-lat/9712013 (1997). https://pith.science/paper/XWS72DUT
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,752 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.30 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.15 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The self-duality transformation is applied to the Fisher zeroes near the critical point in the thermodynamic limit in the q>4 state Potts model in two dimensions. A requirement that the locus of the duals of the zeroes be identical to the dual of the locus of zeroes (i) recovers the ratio of specific heat to internal energy discontinuity at criticality and the relationships between the discontinuities of higher cumulants and (ii) identifies duality with complex conjugation. Conjecturing that all zeroes governing ferromagnetic critical behaviour satisfy the latter requirement, the full locus of Fisher zeroes is shown to be a circle. This locus, together with the density of zeroes is shown to be sufficient to recover the singular form of all thermodynamic functions in the thermodynamic limit.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The self-duality transformation is applied to the Fisher zeroes near the critical point in the thermodynamic limit in the q>4 state Potts model in two dimensions. method 0.81 0.85 0.05 asserted 0.99
s1 A requirement that the locus of the duals of the zeroes be identical to the dual of the locus of zeroes (i) recovers the ratio of specific heat to internal energy discontinuity at criticality and the relationships between the discontinuities of higher cumulants and (ii) identifies duality with complex conjugation. result 0.89 0.79 0.13 asserted 1.00
s2 Conjecturing that all zeroes governing ferromagnetic critical behaviour satisfy the latter requirement, the full locus of Fisher zeroes is shown to be a circle. result 0.94 0.85 0.57 asserted 0.67
s3 This locus, together with the density of zeroes is shown to be sufficient to recover the singular form of all thermodynamic functions in the thermodynamic limit. result 0.94 0.87 0.40 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The self-duality transformation is applied to the Fisher zeroes near the critical point in the thermodynamic limit in the q>4 state Potts model in two dimensions. A requirement that the locus of the duals of the zeroes be identical to the dual of the locus of zeroes (i) recovers the ratio of specific heat to internal energy discontinuity at criticality and the relationships between the discontinuities of higher cumulants and (ii) identifies duality with complex conjugation. Conjecturing that all zeroes governing ferromagnetic critical behaviour satisfy the latter requirement, the full locus of Fisher zeroes is shown to be a circle. This locus, together with the density of zeroes is shown to be sufficient to recover the singular form of all thermodynamic functions in the thermodynamic limit.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

Papers whose main result relates to this one's

How each label was checked · JSON

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.