Deterministic replica-exchange method without pseudo random numbers for simulations of complex systems

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• 作者：Ryo Urano^a ; ^{rurano@tb.phys.nagoya-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Yuko Okamoto^a ; ^b ; ^c ; ^d
• 关键词：Replica-exchange method (REM) ; Simulated tempering (ST) ; Monte Carlo (MC) simulation ; Differential equation ; Gibbs sampling ; Heat-bath method ; Pseudo random numbers ; Ising model
• 刊名：Computer Physics Communications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：197
• 期：Complete
• 页码：128-135
• 全文大小：1201 K

文摘

We propose a replica-exchange method (REM) which does not use pseudo random numbers. For this purpose, we first give a conditional probability for Gibbs sampling replica-exchange method (GSREM) based on the heat bath method. In GSREM, replica exchange is performed by conditional probability based on the weight of states using pseudo random numbers. From the conditional probability, we propose a new method called deterministic replica-exchange method (DETREM) that produces thermal equilibrium distribution based on a differential equation instead of using pseudo random numbers. This method satisfies the detailed balance condition using a conditional probability of Gibbs heat bath method and thus results can reproduce the Boltzmann distribution within the condition of the probability. We confirmed that the equivalent results were obtained by REM and DETREM with two-dimensional Ising model. DETREM can avoid problems of choice of seeds in pseudo random numbers for parallel computing of REM and gives analytic method for REM using a differential equation.