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.
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Trebst, S., Huse, D.A., Gull, E., Katzgraber, H.G., Hansmann, U.H.E., Troyer, M. (2009). Ensemble Optimization Techniques for the Simulation of Slowly Equilibrating Systems. In: Landau, D.P., Lewis, S.P., Schöttler, H.B. (eds) Computer Simulation Studies in Condensed-Matter Physics XIX. Springer Proceedings in Physics, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85625-2_6
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