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, Tc∝(pc-p)^Ψ, then we obtain for p<pc, (1) a characteristic increase Γ~T^-1∕(νz) of the Gr\"uneisen parameter Γ for T>Tc, (2) a sign change in the Ginzburg regime of the classical transition, (3) possibly a peak at Tc, (4) a second increase Γ~-T^-1∕(νz) below Tc for systems above the upper critical dimension, and (5) a saturation of Γ∝1∕(pc-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.