Extended state-space Monte Carlo methods - art. no. 056701

In this paper various extensions of the parallel-tempering algorithm are de veloped and their properties are analyzed. The algorithms are designed to a lleviate quasiergodic sampling in systems which have rough energy landscape s by coupling individual Monte Carlo chains to form a composite chain. As w ith parallel tempering, the procedures are based upon extending the state s pace to include parameters to encourage sampling mobility. One of the drawb acks of the parallel-tempering method is the stochastic nature of the Monte Carlo dynamics in the auxiliary variables which extend the state spate. In this work. the possibility of improving the sampling rate by designing det erministic methods of moving through the parameter space is investigated. T he methods developed in this article, which are based upon a statistical qu enching and heating procedure similar in spirit to simulated annealing, are tested on a simple two-dimensional spin system (xy model) and on a model i n vacuo polypeptide system. In the coupled Monte Carlo chain algorithms, we find that the net mobility of the composite chain is determined by the com petition between the characteristic time of coupling between adjacent chain s and the degree of overlap of their distributions. Extensive studies of al l methods are carried out to obtain optimal sampling conditions. In particu lar, the most efficient parallel-tempering procedure is to attempt to swap configurations after very few Monte Carlo updates of the composite chains. Furthermore, it is demonstrated that, contrary to expectations, the determi nistic procedure does not improve the sampling rate over that of parallel t empering.