### 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), Δ_{4} ≥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) |
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Pages (from-to) | 25-50 |

Number of pages | 26 |

Journal | Journal of Statistical Physics |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - May 1981 |

### Fingerprint

### Keywords

- correlation inequalities
- Critical exponents
- critical-exponent inequalities
- Josephson inequality

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*25*(1), 25-50. https://doi.org/10.1007/BF01008477

**More inequalities for critical exponents.** / Sokal, Alan D.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 25, no. 1, pp. 25-50. https://doi.org/10.1007/BF01008477

}

TY - JOUR

T1 - More inequalities for critical exponents

AU - Sokal, Alan D.

PY - 1981/5

Y1 - 1981/5

N2 - 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.

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 - correlation inequalities

KW - Critical exponents

KW - critical-exponent inequalities

KW - Josephson inequality

UR - http://www.scopus.com/inward/record.url?scp=0010651972&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010651972&partnerID=8YFLogxK

U2 - 10.1007/BF01008477

DO - 10.1007/BF01008477

M3 - Article

VL - 25

SP - 25

EP - 50

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -