Sign change of the Grüneisen parameter and magnetocaloric effect near quantum critical points

We consider the Gr\"uneisen parameter and the magnetocaloric effect near a pressure and magnetic field controlled quantum critical point, respectively. Generically, the Gr\"uneisen parameter (and the thermal expansion) displays a characteristic sign change close to the quantum-critical point signaling an accumulation of entropy. If the quantum critical point is the endpoint of a line of finite temperature phase transitions, T₂ ({p₂-p) }^, then we obtain for pT₂, (2) a sign change in the Ginzburg regime of the classical transition, (3) possibly a peak at T₂, (4) a second increase -T^-1∕ () below T₂ for systems above the upper critical dimension, and (5) a saturation of 1∕ (p₂-p). We argue that due to the characteristic divergencies and sign changes the thermal expansion, the Gr\"uneisen parameter and magnetocaloric effect are excellent tools to detect and identify putative quantum critical points.