A note on the Ising model in high dimensions
(1989) Communications in Mathematical Physics — Vol. 122, n° 4, p. 597-607 (1989)
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- Abstract
- The authors consider the /b d/-dimensional Ising model with a nearest neighbor ferromagnetic interaction /b J/(/b d/)=1/4/b d/. They show that as /b d/ rarr infinity the + phase (and the - phase) approaches a product measure with the density given by the mean field approximation. In particular the spontaneous magnetization converges to its mean field value. A similar result holds for the unique Gibbs measure of the system subject to an external field /b h/ ne 0.
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Bricmont, J., Kesten, H., Lebowitz, J. L., & Schonmann, R. H. (1989). A note on the Ising model in high dimensions. Communications in Mathematical Physics, 122(4), 597-607. https://doi.org/10.1007/BF01256495 (Original work published 1989)