  Monte Carlo simulation techniques, like simulated annealing and parallel
tempering, are often used to evaluate low-temperature properties and find
ground states of disordered systems. Here we compare these methods using direct
calculations of ground states for three-dimensional Ising diluted
antiferromagnets in a field (DAFF) and three-dimensional Ising spin glasses
(ISG). For the DAFF, we find that, with respect to obtaining ground states,
parallel tempering is superior to simple Monte-Carlo and to simulated
annealing. However, equilibration becomes more difficult with increasing
magnitude of the externally applied field. For the ISG with bimodal couplings,
which exhibits a high degeneracy, we conclude that finding true ground states
is easy for small systems, as is already known. But finding each of the
degenerate ground states with the same probability (or frequency), as required
by Boltzmann statistics, is considerably harder and becomes almost impossible
for larger systems.
