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If N classical particles in two dimensions interacting through a pair potential (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 (r) -r^2|^2 (r) | is integrable at r= and positive and nonintegrable at r=0, both for =0 and for some positive. 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.
N. David Mermin (Thu,) studied this question.