Topological disorder hierarchically trapped at frustration sites: Physical picture for a glass

A dynamical picture for glass is illustrated by a two-dimensional Josephson-junction-array model in an overall neutral flux distribution {${\Phi }_I$}, ${\mathcal{J}}_I$ ${\Phi }_I$=0 that is of a self-similar, hierarchical type. A non- equilibrium ±1 vortex population, trapped at low temperatures T on {${\Phi }_I$}, can annihilate only in a sequential, slow ∼$t^{\mathrm{-}T}$ manner, implying long-lived glassy behavior. Vortex accumulation sets in on cooling at a temperature $T_G$(Ṫ) logarithmically dependent on the cooling rate Ṫ.