We present a numerical study of thermodynamical properties of dimerized frustrated Heisenberg chains down to extremely low temperatures with applications to CuGeO 3 . A variant of the finite temperature density matrix renormalization group ͑DMRG͒ allows the study of the dimerized phase previously unaccessible to ab initio calculations. We investigate static dimerized systems as well as the instability of the quantum chain towards lattice dimerization. The crossover from a quadratic response in the free energy to the distortion field at finite temperature to nonanalytic behavior at zero temperature is studied quantitatively. Various physical quantities are derived and compared with experimental data for CuGeO 3 such as magnetic dimerization, critical temperature, susceptibility, and entropy.

The theory by Cross and Fisher (CF) is by now commonly accepted for the description of the spinPeierls 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.