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Absence of long-range order with long-range potentials

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Abstract

A particular form of Mermin's inequality is analyzed for repulsive inverse power potentials [V(r)=e 2 r −m/m] in ad-dimensional space. For long-range potentials (m ≤ d) the system is put into a stabilizing background. Long-range order is shown to be excluded ford ≤ (m + 2)/2 whenm ≤ d, while for short-range potentials (m > d) we recover Mermin's result (d ≤ 2). For Coulomb systems (m=d − 2) and the experimentally studied electron surface layer (d = 2,m=1), long-range order cannot be excluded by the present argument.

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Authors and Affiliations

  1. Chimie-Physique II, Université Libre de Bruxelles, Bruxelles, Belgium

    Marc Baus

  2. Chercheur Qualifié du Fonds National Belge de la Recherche Scientifique, Belgium

    Marc Baus

Authors
  1. Marc Baus
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Baus, M. Absence of long-range order with long-range potentials. J Stat Phys 22, 111–119 (1980). https://doi.org/10.1007/BF01007993

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