Nonlocal Potentials and Crystalline Order in One and Two Dimensions

We revisit the seminal 1968 proof of the absence of crystalline order in two dimensions and analyze the importance played in the quantum theorem by the assumption of local pair potentials. We relax the assumption of local potentials and consider instead nonlocal pair potentials. We show that the 1/k...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Author: Alexanian, Moorad
Format: Article
Language:English
Subjects:
Two dimensional analysis
Online Access:Get full text
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Summary:We revisit the seminal 1968 proof of the absence of crystalline order in two dimensions and analyze the importance played in the quantum theorem by the assumption of local pair potentials. We relax the assumption of local potentials and consider instead nonlocal pair potentials. We show that the 1/k2-singularity that occurs in the Bogoliubov inequality, which leads to no crystalline order in two dimensions for local potentials and nonzero temperatures, does not occur for nonlocal potentials. Accordingly, crystalline order in one and two dimensions cannot be ruled out for nonlocal pair potentials at finite temperatures.
ISSN:2331-8422
DOI:10.48550/arxiv.2312.05111