Abstract
It is proved that an infinite linear chain of spins μ j =±1, with an interaction energy
has zero spontaneous magnetization at all finite temperatures, provided thatJ (n) is non-negative and that
. This shows that a theorem ofRuelle, establishing the absence of long-range order when the sum Σn J (n) converges, is not the best possible.
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References
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Dyson, F.J. Non-existence of spontaneous magnetization in a one-dimensional Ising ferromagnet. Commun.Math. Phys. 12, 212–215 (1969). https://doi.org/10.1007/BF01661575
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DOI: https://doi.org/10.1007/BF01661575