  Parisi's formal replica-symmetry--breaking (RSB) scheme for mean-field spin
glasses has long been interpreted in terms of many pure states organized
ultrametrically. However, the early version of this interpretation, as applied
to the short-range Edwards-Anderson model, runs into problems because as shown
by Newman and Stein (NS) it does not allow for chaotic size dependence, and
predicts non-self-averaging that cannot occur. NS proposed the concept of the
metastate (a probability distribution over infinite-size Gibbs states in a
given sample that captures the effects of chaotic size dependence) and a
non-standard interpretation of the RSB results in which the metastate is
non-trivial and is responsible for what was called non-self-averaging. Here we
use the effective field theory of RSB, in conjunction with the rigorous
definitions of pure states and the metastate in infinite-size systems, to show
that the non-standard picture follows directly from the RSB mean-field theory.
In addition, the metastate-averaged state possesses power-law correlations
throughout the low temperature phase; the corresponding exponent $\zeta$ takes
the value $4$ according to the field theory in high dimensions $d$, and
describes the effective fractal dimension of clusters of spins. Further, the
logarithm of the number of pure states in the decomposition of the
metastate-averaged state that can be distinguished if only correlations in a
window of size $W$ can be observed is of order $W^{d-\zeta}$. These results
extend the non-standard picture quantitatively; we show that arguments against
this scenario are inconclusive.
