Spin-glass dynamics

The configuration space of spin-glasses is characterized by the existence of quasi-degenerate equilibrium states separated by barriers, Δ(T). A temperature cycling protocol enables us to extract the temperature dependence of a specific barrier. We determine ϖΔ(T)/ϖT vs T, and ϖΔ(T)/ϖT vs Δ for barriers between 25Tg and 35Tg at temperatures 8, 9, 9.5 and 10 K (Tg = 10.4 K) for Ag:Mn (2.6 at%). We find, in the range of temperature investigated and within experimental accuracy, that ϖΔ(T)/ϖT depends only on the particular value of Δ(T) and not on the temperature. dΔ(T)/dTr can be fitted using all the data points to either a power law (aΔ6) or an exponential [α exp(βΔ)], where r = T/Tg. Integration leads to a divergence of Δ(T) at temperature T∗ (integration constant) as the temperature decreases, characteristic of the particular barrier considered. The existence of aging effects at all temperatures below Tg in the whole range of accessible times impliesa continuous distribution of barrier heights at any temperature. Hence, at any temperature below Tg there are diverging barriers, associated with a distribution of T∗ with an upper cutoff value of Tg. Said another way, as the temperature is lowered to Tg, the first divergence of a barrier occurs, separating phase space into two (or more) regimes. States separated by divergent barriers are the “pure states”. As the temperature is lowered, a continuous series of barrier divergences breaks up phase space into ever smaller regions, creating an ever increasing number of pure states. Between these divergent barriers, barriers of finite height exist. Those between 25Tg and 35Tg are responsible for the dynamics accessible to us in our experiments.