SPIN-GLASS DYNAMICS ON A HIERARCHICAL TREE

The configuration space of spin glasses is characterized by the existence of quasi-degenerate equilibrium states separated by barriers, DELTA(T). A temperature cycling protocol allows extraction of the temperature dependence of a specific barrier. We find partial derivative DELTA(T)/partial derivative T depends only on the particular value of DELTA(T) and not on the temperature. Using either a power law or an exponential fit (either is equally accurate), integration leads to a divergence of DELTA(T) at a particular temperature T(not-equal) as the temperature decreases, characteristic of the particular barrier considered. This is interpreted as a continuous divergence of barriers as the temperature is lowered, beginning at T(g). Between these divergent barriers, barriers of finite height exist. The time decay of the thermoremanent magnetization at measurement times t much greater than the waiting time t(w) is a measure of the correlation of the spin glass at time t with the field-cooled state. Using ultrametricity, this enables the extraction of the branching ratio of the ''tree'' according to which the spin glass states we organized. Experiments are interpreted in terms of a constant branching ratio for the ultrametric tree within the (small) range of overlaps accessible because of the experimental time window.