Decay of Order in Classical Many-Body Systems. III. Ising Model at Low Temperature
- 1 April 1973
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 7 (7), 3187-3203
- https://doi.org/10.1103/physrevb.7.3187
Abstract
In this work the decay of correlation in the -dimensional Ising model is studied at low temperatures as a function of dimensionality of the lattice and magnetic field . Except for the special case of the two-dimensional zero-field nearest-neighbor lattices, the decay of correlation verifies the Ornstein-Zernike prediction . For the two-dimensional zero-field case, the Ornstein-Zernike form is replaced by the "anomalous" form . This "anomalous" result is shown to arise from the peculiarities of the spectrum of the transfer matrix in this case and is replaced by the Ornstein-Zernike result when further-neighbor forces are present. The results presented herein agree with the previously obtained exact results for the zero-field two-dimensional Ising model.
Keywords
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