Abstract

Lattice vibrations in finite discrete systems with the symmetric boundary condition are studied using the Tilley–Zeks model with emphasis on the effect of the discreteness of the lattice. It is found that the normal modes, the soft-mode frequency and the transition temperature all depend strongly on the lattice constant a , which expresses the degree of discreteness. It is pointed out that, in a small system with a few lattices, the effect of the discontinuity of the lattice cannot be ignored.

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