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A projected entropy controller for transition matrix calculations

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Abstract

We define the projected entropy S(T) at a given temperature T in the context of an Ising model transition matrix calculation as the entropy associated with the distribution of Markov-chain realizations in energy-magnetization, E–H, space. An even sampling of states is achieved by accumulating the results from multiple Markov chains while decrementing 1∕T at a rate proportional to the inverse of the effective number, exp(S(T)), of accessible projected states. Such a procedure is both highly accurate and far simpler to implement than a previously suggested method based on monitoring the evolution of the E–H distribution at each temperature [D. Yevick, Y.-H. Lee, Eur. Phys. J. B 90, 81 (2017)]. We further demonstrate a transition matrix procedure that instead ensures uniform sampling in physical entropy.

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Correspondence to David Yevick.

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Yevick, D. A projected entropy controller for transition matrix calculations. Eur. Phys. J. B 91, 221 (2018). https://doi.org/10.1140/epjb/e2018-90171-0

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Keywords

  • Computational Methods