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More inequalities for critical exponents

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Abstract

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

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Authors and Affiliations

  1. Department of Physics, Princeton University, 08544, Princeton, New Jersey

    Alan D. Sokal

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  1. Alan D. Sokal
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Additional information

NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.

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Sokal, A.D. More inequalities for critical exponents. J Stat Phys 25, 25–50 (1981). https://doi.org/10.1007/BF01008477

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