Thermal expansion and Gruneisen parameter in quantum Griffiths phases

We consider the behavior of the Gruneisen parameter, the ratio between thermal expansion and specific heat, at pressure-tuned infinite-randomness quantum-critical points and in the associated quantum Griffiths phases. We find that the Gruneisen parameter diverges as 1n(T-0/T) with vanishing temperature T in the quantum Griffiths phases. At the infinite-randomness critical point itself, the Gruneisen parameter behaves as [1n(T-0/T)](1+1/(nu psi)) where nu and psi are the correlation length and tunneling exponents. Analogous results hold for the magnetocaloric effect at magnetic-field-tuned transitions. We contrast clean and dirty systems, we discuss subtle differences between Ising and Heisenberg symmetries, and we relate our findings to recent experiments on CePd1-xRhx.