Multicanonical Algorithm, Simulated Tempering, Replica-Exchange Method, and All That

Ayori Mitsutake; Yuko Okamoto

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arXiv · 0810.1117

Multicanonical Algorithm, Simulated Tempering, Replica-Exchange Method, and All That

Ayori Mitsutake·Yuko Okamoto

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Abstract

We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function $E_0$ by adding any physical quantity $V$ of interest as a new energy term with a coupling constant $λ$. We then perform a multi-dimensional multicanonical simulation where a random walk in $E_0$ and $V$ space is realized. We can alternately perform a multi-dimensional simulated tempering simulation where a random walk in temperature $T$ and parameter $λ$ is realized. The results of the multi-dimensional replica-exchange simulations can be used to determine the weight factors for these multi-dimensional multicanonical and simulated tempering simulations.

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Ayori Mitsutake, Yuko Okamoto. 2008-10-07. Multicanonical Algorithm, Simulated Tempering, Replica-Exchange Method, and All That. https://arxiv.org/abs/0810.1117

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