  A simple geometrical characterization of configuration space neighborhoods of
local energy minima in spin glass landscapes is found by exhaustive search.
Combined with previous Monte Carlo investigations of thermal domain growth, it
allows a discussion of the connection between real and configuration space
descriptions of low temperature relaxational dynamics. We argue that the part
of state-space corresponding to a single growing domain is adequately modeled
by a hierarchically organized set of states and that thermal (meta)stability in
spin glasses is related to the nearly exponential local density of states
present within each trap.
