  Using Monte Carlo simulations, we study in detail the overlap distribution
for individual samples for several spin-glass models including the
infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson
models in three and four space dimensions, and one-dimensional long-range
models with diluted power-law interactions. We study three long-range models
with different powers as follows: the first is approximately equivalent to a
short-range model in three dimensions, the second to a short-range model in
four dimensions, and the third to a short-range model in the mean-field regime.
We study an observable proposed earlier by some of us which aims to distinguish
the "replica symmetry breaking" picture of the spin-glass phase from the
"droplet picture," finding that larger system sizes would be needed to
unambiguously determine which of these pictures describes the low-temperature
state of spin glasses best, except for the Sherrington-Kirkpatrick model which
is unambiguously described by replica symmetry breaking. Finally, we also study
the median integrated overlap probability distribution and a typical overlap
distribution, finding that these observables are not particularly helpful in
distinguishing the replica symmetry breaking and the droplet pictures.
