Thermal Expansion and Grüneisen Parameter in Quantum Griffiths Phases
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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 (T0 /T) with vanishing temperature T in the quantum Griffiths phases. at the infinite-randomness critical point itself, the Grüneisen parameter behaves as [ln (T0 /T)]1+1/ (νψ) where ν and ψ 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.