Activated Scaling of Classical and Quantum Spin Glasses

Abstract

A model for thermally activated dynamics in disordered systems shows that the linear and nonlinear susceptibility follows a generic exponential form with a ``critical rounding,'' ${\ensuremath{\chi}}_{1}\ensuremath{\propto}{\ensuremath{\chi}}_{3}\ensuremath{\propto}[T\mathrm{ln}(t/{\ensuremath{\tau}}_{0}^{\ensuremath{'}})/K{]}^{\ensuremath{\gamma}/b\ensuremath{\phi}}\mathrm{exp}\ensuremath{-}[Tt_{g}{}^{\ensuremath{\phi}b}\mathrm{ln}(t/{\ensuremath{\tau}}_{0}^{\ensuremath{'}})/K){]}^{\ensuremath{\nu}/b}$ ($T=\mathrm{\text{temperature}}$, $t=\mathrm{\text{time}}$, $K=\mathrm{\text{barrier constant}}$, ${t}_{g}=1\ensuremath{-}{T}_{\mathrm{SG}}/T$, and ${T}_{\mathrm{SG}}=\mathrm{\text{transition temperature}}$; $\ensuremath{\gamma}>0$ for ${\ensuremath{\chi}}_{3}$ and $<0$ for ${\ensuremath{\chi}}_{1}$). This model, also valid in the presence of resonant tunneling states at energies ${K}_{0}\ensuremath{\ll}K$ [provided that $K$ is replaced by ${K}_{0}+2T\mathrm{ln}$ ($1/{\ensuremath{\Gamma}}_{0}$), where $\ensuremath{\Gamma}_{0}{}^{2}\ensuremath{\propto}$ tunnel splitting of a spin $S=1$], is potentially applicable to a wide variety of systems opening the way for the study of thermally activated quantum phase transitions. The famous spin-glass system ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}$ seems to follow this model.