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http://prola.aps.org/abstract/PR/v158/i2/p383_1
Existence of Long-Range Order in One and Two Dimensions

It is pointed out that a rigorous inequality first proved by Bogoliubov may be used to rule out the existence of quasi-averages (or long-range order) in Bose and Fermi systems for one and two dimensions and T¡Ù0.



http://prola.aps.org/abstract/PR/v187/i2/p732_1
Long-Range Order in One-Dimensional Ising Systems


The argument of Landau and Lifshitz for the absence of long-range order in one-dimensional systems is used to show that order is absent if the interaction energy falls off faster than n-2. When the interaction falls off as n-2, the order cannot go continuously to zero.

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