Thermal expansion and Grueneisen parameter in quantum Griffiths phases

Abstract

We consider the behavior of the Grüneisen 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 Grüneisen parameter diverges as $\ln (T_0/T)$ with vanishing temperature $T$ in the quantum Griffiths phases. At the infinite-randomness critical point itself, the Grüneisen parameter behaves as $[\ln (T_0/T){]}^{1+1/(\nu \psi )}$ 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 CePd${}_{1-x}$Rh${}_x$.

4 pages, 1 eps figure embedded, final version as published

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