Lattice vibrations in finite systems with boundary conditions given with the extrapolation length: II. Discrete model with symmetric boundary condition

摘要

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.