More inequalities for Ising ferromagnets

Research output: Contribution to journalArticle

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Abstract

We consider an Ising spin system with ferromagnetic pair interactions. Combining the old Griffiths inequalities with the recent Fortuin-Kasteleyn-Ginibre inequalities we obtain some new bounds on the correlations and thermodynamic functions. These bounds appear to be of interest in the neighborhood of the two-phase region of these systems, ββc, h∼0 (βc is the reciprocal of the critical temperature, and h is the external magnetic field), where they yield relations between singularities in the spontanuous magnetization m*(β) and the susceptibility χ (β,h): e.g., m*(β) is upper semicontinuous, and a discontinuity in m*(β) at β0 implies that the susceptibility cannot be bounded (near h=0) by an integrable function of h as β→β0 from the left. We also find some inequalities among the critical indices.

Original languageEnglish (US)
Pages (from-to)2538-2541
Number of pages4
JournalPhysical Review B
Volume5
Issue number7
DOIs
StatePublished - Jan 1 1972
Externally publishedYes

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Ferromagnet
Ising
Susceptibility
Upper Semicontinuous
Spin Systems
Critical Temperature
Magnetization
External Field
Discontinuity
Thermodynamics
Magnetic Field
Singularity
Imply
Interaction

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Cite this

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abstract = "We consider an Ising spin system with ferromagnetic pair interactions. Combining the old Griffiths inequalities with the recent Fortuin-Kasteleyn-Ginibre inequalities we obtain some new bounds on the correlations and thermodynamic functions. These bounds appear to be of interest in the neighborhood of the two-phase region of these systems, ββc, h∼0 (βc is the reciprocal of the critical temperature, and h is the external magnetic field), where they yield relations between singularities in the spontanuous magnetization m*(β) and the susceptibility χ (β,h): e.g., m*(β) is upper semicontinuous, and a discontinuity in m*(β) at β0 implies that the susceptibility cannot be bounded (near h=0) by an integrable function of h as β→β0 from the left. We also find some inequalities among the critical indices.",
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More inequalities for Ising ferromagnets. / Lebowitz, Joel L.

In: Physical Review B, Vol. 5, No. 7, 01.01.1972, p. 2538-2541.

Research output: Contribution to journalArticle

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