Thermodynamics of the coupled spin-dimer system TlCuCl3 close to a quantum phase transition

We present thermal expansion alpha, magnetostriction and specific heat C measurements of \tal, which shows a quantum phase transition from a spin-gap phase to a Neel-ordered ground state as a function of magnetic field around H_{C0}->4.8T. Using Ehrenfest's relation, we find huge pressure dependencies of the spin gap for uniaxial as well as for hydrostatic pressure. For T->0 and H->H_{C0} we observe a diverging Grueneisen parameter Gamma(T)=alpha/C, in qualitative agreement with theoretical predictions. However, the predicted individual temperature dependencies alpha(T) and C(T) are not reproduced by our experimental data.