Universally diverging Grueneisen parameter and the magnetocaloric effect close to quantum critical points

Abstract

At a generic quantum critical point, the thermal expansion $\alpha$ is more singular than the specific heat $c_p$. Consequently, the "Grüneisen ratio'', $\GE=α/c_p$, diverges. When scaling applies, $\GE \sim T^{-1/(νz)}$ at the critical pressure $p=p_c$, providing a means to measure the scaling dimension of the most relevant operator that pressure couples to; in the alternative limit $T\to 0$ and $p\ne p_c$, $\GE \sim \frac{1}{p-p_c}$ with a prefactor that is, up to the molar volume, a simple {\it universal} combination of critical exponents. For a magnetic-field driven transition, similar relations hold for the magnetocaloric effect $(1/T)\partial T/\partial H{|}_S$. Finally, we determine the corrections to scaling in a class of metallic quantum critical points.

4 pages, 1 figure; general discussion on how the Grueneisen exponent measures the scaling dimension of the most relevant operator at any QCP is expanded