More inequalities for critical exponents

Alan D. Sokal

doi:10.1007/BF01008477

More inequalities for critical exponents

Alan D. Sokal

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

Abstract

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequality dv′ ≥γ′+2 β ≥ 2-α′. Others are 1 ≤γ′ ≤ 1 +v′_φ, 1 ≤ζ ≤ 1 δμ_φ, δ ≥ 1, dμ_φ ≥ 1 + 1/δ (for φ ≥d), dv′_φ, ≥ Δ′₃ + α (for φ ≥d), Δ₄ ≥γ, and Δ_2m ≤ Δ_2m+2 (for m ≥ 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.

Original language	English (US)
Pages (from-to)	25-50
Number of pages	26
Journal	Journal of Statistical Physics
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/BF01008477
State	Published - May 1981

Keywords

Critical exponents
Josephson inequality
correlation inequalities
critical-exponent inequalities

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01008477

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title = "More inequalities for critical exponents",

abstract = "A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequality dv′ ≥γ′+2 β ≥ 2-α′. Others are 1 ≤γ′ ≤ 1 +v′φ, 1 ≤ζ ≤ 1 δμφ, δ ≥ 1, dμφ ≥ 1 + 1/δ (for φ ≥d), dv′φ, ≥ Δ′3 + α (for φ ≥d), Δ4 ≥γ, and Δ2m ≤ Δ2m+2 (for m ≥ 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.",

keywords = "Critical exponents, Josephson inequality, correlation inequalities, critical-exponent inequalities",

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AB - A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequality dv′ ≥γ′+2 β ≥ 2-α′. Others are 1 ≤γ′ ≤ 1 +v′φ, 1 ≤ζ ≤ 1 δμφ, δ ≥ 1, dμφ ≥ 1 + 1/δ (for φ ≥d), dv′φ, ≥ Δ′3 + α (for φ ≥d), Δ4 ≥γ, and Δ2m ≤ Δ2m+2 (for m ≥ 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.

KW - Critical exponents

KW - Josephson inequality

KW - correlation inequalities

KW - critical-exponent inequalities

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JF - Journal of Statistical Physics

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More inequalities for critical exponents

Abstract

Keywords

ASJC Scopus subject areas

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