Crystalline Order in Two Dimensions

N. D. Mermin
Phys. Rev. 176, 250 – Published 5 December 1968; Errata Phys. Rev. B 20, 4762 (1979); Phys. Rev. B 74, 149902 (2006)
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Abstract

If N classical particles in two dimensions interacting through a pair potential Φ(r) are in equilibrium in a parallelogram box, it is proved that every k0 Fourier component of the density must vanish in the thermodynamic limit, provided that Φ(r)λr2|2Φ(r)| is integrable at r= and positive and nonintegrable at r=0, both for λ=0 and for some positive λ. This result excludes conventional crystalline long-range order in two dimensions for power-law potentials of the Lennard-Jones type, but is inconclusive for hard-core potentials. The corresponding analysis for the quantum case is outlined. Similar results hold in one dimension.

  • Received 1 July 1968

DOI:https://doi.org/10.1103/PhysRev.176.250

©1968 American Physical Society

Errata

Authors & Affiliations

N. D. Mermin*

  • Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York

  • *Alfred P. Sloan Foundation Fellow.

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Vol. 176, Iss. 1 — December 1968

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