Exact, numerical, and mean field behavior of a dimerizing lattice in one   dimension
  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, correlation length, and order parameter are calculated three ways: (a) by mean field approximation, (b) by numerical molecular dynamics simulation, and (c) by an exact transfer matrix method. The single-particle spectrum (velocity-velocity correlation function) is found numerically and in mean field theory. 
Vasili Perebeinos, Philip B. Allen and James Napolitano