  We revisit the problem of the spin-Peierls instability in a one dimensional
spin-1/2 chain coupled to phonons. The phonons are treated within the mean
field approximation. We use bosonization techniques to describe the gapped spin
chain and then use the Thermodynamic Bethe Ansatz to obtain quantitative
results for the thermodynamics of the spin-Peierls system in a whole range of
temperature. This allows us to predict the behavior of the specific heat and
the magnetic susceptibility in the entire dimerized phase. We study the effect
of small magnetic fields on the transition. Moreover, we obtain the parameters
of the Landau-Ginzburg theory describing this continuous phase transition near
the critical point.
