  Competing phases or interactions in complex many-particle systems can result
in free energy barriers that strongly suppress thermal equilibration. Here we
discuss how extended ensemble Monte Carlo simulations can be used to study the
equilibrium behavior of such systems. Special focus will be given to a recently
developed adaptive Monte Carlo technique that is capable to explore and
overcome the entropic barriers which cause the slow-down. We discuss this
technique in the context of broad-histogram Monte Carlo algorithms as well as
its application to replica-exchange methods such as parallel tempering. We
briefly discuss a number of examples including low-temperature states of
magnetic systems with competing interactions and dense liquids.
