  We present results from Monte Carlo simulations of the one-dimensional Ising
spin glass with power-law interactions at low temperature, using the parallel
tempering Monte Carlo method. For a set of parameters where the long-range part
of the interaction is relevant, we find evidence for large-scale droplet-like
excitations with an energy that is independent of system size, consistent with
replica symmetry breaking. We also perform zero-temperature defect energy
calculations for a range of parameters and find a stiffness exponent for domain
walls in reasonable, but by no means perfect agreement with analytic
predictions.
