Local Ward identities and the decay of correlations in ferromagnets |
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Authors: | Michael Aizenman Barry Simon |
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Institution: | (1) Department of Physics, Princeton University, 08544 Princeton, NJ, USA;(2) Department of Mathematics, Princeton University, USA |
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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 allN2 and some forN=2, 3, 4. These are used to prove a mass gap above the mean field temperature, for allN2. ForN=2, 3, 4 we prove an upper bound on a critical exponent, and a lower bound on the susceptability which diverges asm0.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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