  The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick
Ising spin glasses are studied via large-scale Monte Carlo simulations at low
temperatures, deep within the spin-glass phase. Performing a careful
statistical analysis of several thousand independent disorder realizations and
using an observable that detects peaks in the overlap distribution, we show
that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly
different low-temperature behavior. The structure of the spin-glass overlap
distribution for the Edwards-Anderson model suggests that its low-temperature
phase has only a single pair of pure states.
