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Spatially local parallel tempering for thermal-equilibrium sampling
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Parallel tempering (PT) is a set of techniques for accelerating thermal-equilibrium sampling in systems where the exploration of configuration space is hindered by energy barriers. With standard PT algorithms, the computational effort scales unfavorably with system size, so that it is difficult to apply them to large systems. We propose local PT algorithms, for which the computational effort is proportional to the number of degrees of freedom. We demonstrate the effectiveness of the new algorithms on two one-dimensional model systems, showing that results for selected observables are correctly reproduced, and that practical linear scaling is achieved. We show also that the algorithms are readily applied to systems in higher dimensions. We note the prospects for studying large extended systems, including surfaces and interfaces.
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