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Geometry of contours and Peierls estimates in d=1 Ising models

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M. Cassandro, P.A. Ferrari, I. Merola, E. Presutti

Mathematical Physics · Submitted 25 Nov 2002

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

The authors' main claim This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures.

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arXiv IDmath-ph/0211062 (version 2)
Pith ID24ENRZFX, Pith's permanent record of this paper and its review
CitationE. Presutti, I. Merola, M. Cassandro, P.A. Ferrari. "Geometry of contours and Peierls estimates in d=1 Ising models." arXiv:math-ph/0211062 (2002). https://pith.science/paper/24ENRZFX
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,973 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.54 · compares with prior results 0.67 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. We introduce a geometric description of the spin configurations in terms of triangles which play the role of contours and for which we establish Peierls bounds. This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures.

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 Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. background 0.84 0.45 0.03 asserted 0.90
s1 We introduce a geometric description of the spin configurations in terms of triangles which play the role of contours and for which we establish Peierls bounds. contribution 0.62 0.95 0.15 asserted 1.00
s2 This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures. interpretation 0.54 0.81 0.61 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from proof or derivation 1.00.

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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

Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. We introduce a geometric description of the spin configurations in terms of triangles which play the role of contours and for which we establish Peierls bounds. This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures.

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