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

Abstract

The thermodynamics and dynamics of a one-dimensional dimer-forming anharmonic model is studied in the classical limit. This model mimics the behavior of materials with a Peierls instability. Specific heat C( T), correlation length l c( T), and order parameter are calculated in three ways: (a) by mean-field (MF) approximation, (b) by numerical molecular dynamics (MD) simulation, and (c) by an exact transfer matrix method. The neighbor distribution function F( x) and vibrational density-of-states D( ω) (Fourier transform of velocity–velocity correlation function) are found numerically. MF theory fails completely to describe the destruction of long-range order by fluctuations, but nevertheless, the MF answers for C( T), l c( T), F( x), and D( ω) give helpful interpretations of the exact behavior.