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At a generic quantum critical point, the thermal expansion $\alpha$ is moresingular than the specific heat $c_p$. Consequently, the "Gr\"uneisen ratio'',$\GE=\alpha/c_p$, diverges. When scaling applies, $\GE \sim T^{-1/(\nu z)}$ atthe critical pressure $p=p_c$, providing a means to measure the scalingdimension of the most relevant operator that pressure couples to; in thealternative limit $T\to0$ and $p \ne p_c$, $\GE \sim \frac{1}{p-p_c}$ with aprefactor that is, up to the molar volume, a simple {\it universal} combinationof critical exponents. For a magnetic-field driven transition, similarrelations hold for the magnetocaloric effect $(1/T)\partial T/\partial H|_S$.Finally, we determine the corrections to scaling in a class of metallic quantumcritical points.Comment: 4 pages, 1 figure; general discussion on how the Grueneisen exponent  measures the scaling dimension of the most relevant operator at any QCP is  expande

Universally Diverging Grüneisen Parameter and the Magnetocaloric Effect Close to Quantum Critical Points