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

At a generic quantum critical point, the thermal expansion alpha is more singular than the specific heat c(p). Consequently, the Gruneisen ratio, Gamma=alpha/c(p), diverges. When scaling applies, Gammasimilar toT(-1/(nuz)) 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-->0 and pnot equalp(c), Gammasimilar to1/(p-p(c)) with a prefactor that is, up to the molar volume, a simple universal combination of critical exponents. For a magnetic-field driven transition, similar relations hold for the magnetocaloric effect (1/T)partial derivativeT/partial derivativeH\(S). Finally, we determine the corrections to scaling in a class of metallic quantum critical points.