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Abstract
For a class of nonnegative, range-1 pair potentials in one-dimensional continuous space we prove that any classical ground state of lower density ⩾1 is a tower-lattice, i.e. a lattice formed by towers of particles the heights of which can differ only by 1, and the lattice constant is 1. The potential may be flat or may have a cusp at the origin; it can be continuous, but its derivative has a jump at 1. The result is valid on finite intervals or rings of integer length and on the whole line.
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