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Decay of correlations in the one dimensional Ising model withJ ij =|i−j|−2

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Abstract

A low temperature expansion is constructed for the one dimensional Ising model with Hamiltonian\(H = \sum\limits_{i< j} {\left| {i - j} \right|^{ - 2} \left( {1 - \sigma _i \sigma _j } \right)} \). It is shown that the two point function 〈σ i ;σ j 〉 obeys upper and lower bounds of the formf(β)|i−j|−2 for inverse temperature β sufficiently large.

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Authors and Affiliations

  1. Department of Physics, Harvard University, 02138, Cambridge, MA, USA

    John Z. Imbrie

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  1. John Z. Imbrie
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Communicated by A. Jaffe

Junior Fellow, Harvard University Society of Fellows. Supported in part by the National Science Foundation under Grant No. PHY79-16812.

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Imbrie, J.Z. Decay of correlations in the one dimensional Ising model withJ ij =|i−j|−2 . Commun.Math. Phys. 85, 491–515 (1982). https://doi.org/10.1007/BF01403501

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  • DOI: https://doi.org/10.1007/BF01403501

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