Skeleton inequalities and mean field properties for lattice spin systems

Takashi Hara; Tetsuya Hattori; Hal Tasaki

doi:10.1063/1.526719

Skeleton inequalities and mean field properties for lattice spin systems

Takashi Hara, Tetsuya Hattori, Hal Tasaki

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We present a proof of skeleton inequalities for ferromagnetic lattice spin systems with potential V(φ²) = (a/2)φ² + Σ_{n = 2}^M {λ_2n/(2n)!} φ²ⁿ (a real, λ_2n ≥0) generalizing the Brydges-Fröhlich-Sokal and Bovier-Felder methods. As an application of the inequalities, we prove that, for sufficiently soft systems in d > 4 dimensions, critical exponents γ, α, and Δ₄ take their mean-field values (i.e., γ = 1, α = 0, and Δ₄ = 3/2).

Original language	English
Pages (from-to)	2922-2929
Number of pages	8
Journal	Journal of Mathematical Physics
Volume	26
Issue number	11
DOIs	https://doi.org/10.1063/1.526719
Publication status	Published - Jan 1 1985
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.526719

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abstract = "We present a proof of skeleton inequalities for ferromagnetic lattice spin systems with potential V(φ2) = (a/2)φ2 + Σn = 2M {λ2n/(2n)!} φ2n (a real, λ2n ≥0) generalizing the Brydges-Fr{\"o}hlich-Sokal and Bovier-Felder methods. As an application of the inequalities, we prove that, for sufficiently soft systems in d > 4 dimensions, critical exponents γ, α, and Δ4 take their mean-field values (i.e., γ = 1, α = 0, and Δ4 = 3/2).",

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AU - Hara, Takashi

AU - Hattori, Tetsuya

AU - Tasaki, Hal

PY - 1985/1/1

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N2 - We present a proof of skeleton inequalities for ferromagnetic lattice spin systems with potential V(φ2) = (a/2)φ2 + Σn = 2M {λ2n/(2n)!} φ2n (a real, λ2n ≥0) generalizing the Brydges-Fröhlich-Sokal and Bovier-Felder methods. As an application of the inequalities, we prove that, for sufficiently soft systems in d > 4 dimensions, critical exponents γ, α, and Δ4 take their mean-field values (i.e., γ = 1, α = 0, and Δ4 = 3/2).

AB - We present a proof of skeleton inequalities for ferromagnetic lattice spin systems with potential V(φ2) = (a/2)φ2 + Σn = 2M {λ2n/(2n)!} φ2n (a real, λ2n ≥0) generalizing the Brydges-Fröhlich-Sokal and Bovier-Felder methods. As an application of the inequalities, we prove that, for sufficiently soft systems in d > 4 dimensions, critical exponents γ, α, and Δ4 take their mean-field values (i.e., γ = 1, α = 0, and Δ4 = 3/2).

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