The configuration space of spin glasses is characterized by the existence of quasidegenerate equilibrium states separated by barriers, ∆(T). A temperature cycling protocol allows extraction of the temperature dependence of a specific barrier. We find ∂∆(T)/∂T depends only on the particular value of ∆(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 ∆(T) at a particular temperature T* 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 Tg. 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 tw 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 are 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.
An algorithm for reconstructing ultrametric tree-child networks from inter-taxa distances