Abstract
If classical particles in two dimensions interacting through a pair potential are in equilibrium in a parallelogram box, it is proved that every Fourier component of the density must vanish in the thermodynamic limit, provided that is integrable at and positive and nonintegrable at , both for 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.
- Received 1 July 1968
DOI:https://doi.org/10.1103/PhysRev.176.250
©1968 American Physical Society