Exact, numerical, and mean field behavior of a dimerizing lattice in one dimension

The thermodynamics and dynamics of a one-dimensional dimer-forming anharmon ic model is studied in the classical limit. This model mimics the behavior of materials with a Peierls instability. Specific heat C(T), correlation le ngth l(c)(T), and order parameter are calculated in three ways: (a) by mean -field (MF) approximation, (b) by numerical molecular dynamics (MD) simulat ion, and (c) by an exact transfer matrix method. The neighbor distribution function F(x) and vibrational density-of-states D(omega) (Fourier transform of velocity-velocity correlation function) are found numerically. MF theor y fails completely to describe the destruction of long-range order by fluct uations, but nevertheless, the MF answers for C(T), l(c)(T), F(x), and D(om ega) give helpful interpretations of the exact behavior. (C) 2001 Published by Elsevier Science Ltd.