  The theory by Cross and Fisher (CF) is by now commonly accepted for the
description of the spin-Peierls transition within an adiabatic approach. The
dimerization susceptibility as the essential quantity, however, is approximated
by means of a continuum description. Several important experimental
observations can not be understood within this scope. Using density matrix
renormalization group (DMRG) techniques we are able to treat the spin system
exactly up to numerical inaccuracies. Thus we find the correct dependence of
the equation of state on the spin-spin interaction constant J, still in an
adiabatic approach. We focus on the pressure dependence of the critical
temperature which is absent in the CF theory as the only energy scale with
considerable pressure dependence is J which drops out completely. Comparing the
theoretical findings to the experimentally measured pressure dependence of the
spin-Peierls temperature we obtain information on the variation of the
frustration parameter with pressure. Furthermore, the ratio of the spectral gap
and the transition temperature is analyzed.
