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

We consider the Grüneisen parameter and the magnetocaloric effect near a pressure and magnetic field controlled quantum critical point, respectively. Generically, the Grüneisen 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, $T_c\propto {(p_c-p)}^{\Psi }$, then we obtain for $p<p_c$, (1) a characteristic increase $\Gamma \sim T^{-1∕\left(\nu z\right)}$ of the Grüneisen parameter $\Gamma$ for $T>T_c$, (2) a sign change in the Ginzburg regime of the classical transition, (3) possibly a peak at $T_c$, (4) a second increase $\Gamma \sim -T^{-1∕\left(\nu z\right)}$ below $T_c$ for systems above the upper critical dimension, and (5) a saturation of $\Gamma \propto 1∕(p_c-p)$. We argue that due to the characteristic divergencies and sign changes the thermal expansion, the Grüneisen parameter and magnetocaloric effect are excellent tools to detect and identify putative quantum critical points.