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On the upper critical dimensions of random spin systems

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Abstract

A set of critical exponent inequalities is proved for a large class of classical random spin systems. The inequalities imply rigorous (and probably the optimal) lower bounds for the upper critical dimensions, i.e.,d u≥4 for regular and random ferromagnets,d u≥6 for spin glasses and random field systems.

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  1. Hal Tasaki

    Present address: Department of Physics, Gakushuin University, Mejiro, Toshima-ku, 171, Tokyo, Japan

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

    Hal Tasaki

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  1. Hal Tasaki
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Tasaki, H. On the upper critical dimensions of random spin systems. J Stat Phys 54, 163–170 (1989). https://doi.org/10.1007/BF01023476

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