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Local Ward identities and the decay of correlations in ferromagnets

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Abstract

Using local Ward identities we prove a number of correlation inequalities forN-component, isotropically coupled, pair interacting ferromagnets; some for allN≧2 and some forN=2, 3, 4. These are used to prove a mass gap above the mean field temperature, for allN≧2. ForN=2, 3, 4 we prove an upper bound on a critical exponent, and a lower bound on the susceptability which diverges asm→0.

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Authors and Affiliations

  1. Department of Physics, Princeton University, 08544, Princeton, NJ, USA

    Michael Aizenman & Barry Simon

  2. Department of Mathematics, Princeton University, USA

    Barry Simon

Authors
  1. Michael Aizenman
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  2. Barry Simon
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Additional information

Communicated by A. Jaffe

Research partially supported by US National Science Foundation under Grant PHY-7825390 A01.

Research partially supported by US National Science Foundation under Grant MCS-78-01885.

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Aizenman, M., Simon, B. Local Ward identities and the decay of correlations in ferromagnets. Commun.Math. Phys. 77, 137–143 (1980). https://doi.org/10.1007/BF01982713

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