Ensemble dependence of the critical behavior of a system with long-range interaction and quenched randomness

Nir Schreiber; Reuven Cohen; Simi Haber

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Ensemble dependence of the critical behavior of a system with long-range interaction and quenched randomness

Nir Schreiber, Reuven Cohen, Simi Haber

Statistical Mechanics · Submitted 27 Aug 2022

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

The authors' main claim It is found, by varying the concentration of the Ising spins, that the model displays different phase portraits in concentration-temperature parameter space, within the canonical and the microcanonical ensembles.

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arXiv ID2208.12965 (version 2)

Pith IDB5GKH7VN, Pith's permanent record of this paper and its review

CitationNir Schreiber, Reuven Cohen, Simi Haber. "Ensemble dependence of the critical behavior of a system with long-range interaction and quenched randomness." arXiv:2208.12965 (2022). https://pith.science/paper/B5GKH7VN

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,022 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.10 · states quantitative result 0.05 · compares with prior results 0.13 · mentions code or data availability 0.02.

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We propose a hybrid model governed by the Blume-Emery-Griffiths (BEG) Hamiltonian with a mean-field-like interaction, where the spins are randomly quenched such that some of them are "pure" Ising and the others admit the BEG set of states. It is found, by varying the concentration of the Ising spins, that the model displays different phase portraits in concentration-temperature parameter space, within the canonical and the microcanonical ensembles. Phenomenological indications that these portraits are rich and rather unusual are provided.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We propose a hybrid model governed by the Blume-Emery-Griffiths (BEG) Hamiltonian with a mean-field-like interaction, where the spins are randomly quenched such that some of them are "pure" Ising and the others admit the BEG set of states.	contribution 0.71	0.72	0.06	asserted 0.94
s1	It is found, by varying the concentration of the Ising spins, that the model displays different phase portraits in concentration-temperature parameter space, within the canonical and the microcanonical ensembles.	result 1.00	0.93	0.62	asserted 1.00
s2	Phenomenological indications that these portraits are rich and rather unusual are provided.	interpretation 0.61	0.73	0.11	hedged possibility 0.84

What kind of paper the classifier reports this is: theoretical result 0.84 · evidence from simulation or computation 0.82.

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Original abstract

We propose a hybrid model governed by the Blume-Emery-Griffiths (BEG) Hamiltonian with a mean-field-like interaction, where the spins are randomly quenched such that some of them are "pure" Ising and the others admit the BEG set of states. It is found, by varying the concentration of the Ising spins, that the model displays different phase portraits in concentration-temperature parameter space, within the canonical and the microcanonical ensembles. Phenomenological indications that these portraits are rich and rather unusual are provided.

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In some sense, a similar phenomenon has been recently detected in another hybrid ($q$-state Potts) model [ref] where, in the large $q$ limit, the system benefits from the presence of very small concentrations of “second order” spins [ref] ; this way avoids a first order transition that would have occurred if those spins where absent [ref] .

Discontinuity of the phase transition for the planar random-cluster and Potts models with $q>4$ · Concluding remarks · 0.90

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