TY - JOUR

T1 - Deterministic replica-exchange method without pseudo random numbers for simulations of complex systems

AU - Urano, Ryo

AU - Okamoto, Yuko

N1 - Funding Information:
We are grateful to Drs. Yoshiharu Mori and Tetsuro Nagai for informing us the existence of Ref. [33] . Some of the computations were performed on the supercomputers at the Institute for Molecular Science, at the Supercomputer Center, Institute for Solid State Physics, University of Tokyo, and Center for Computational Sciences, University of Tsukuba. This work was supported, in part, Grants-in-Aid for Scientific Research (A) (No. 25247071 ), for Scientific Research on Innovative Areas (“Dynamical Ordering & Integrated Functions”), Program for Leading Graduate Schools “Integrative Graduate Education and Research in Green Natural Sciences”, and for the Computational Materials Science Initiative, for High Performance Computing Infrastructure, and CREST “Molecular Technology for Chemical Control of Epigenetics towards Drug Discovery” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan and Japan Science and Technology Agency (JST) .
Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

KW - Differential equation

KW - Gibbs sampling

KW - Heat-bath method

KW - Ising model

KW - Monte Carlo (MC) simulation

KW - Pseudo random numbers

KW - Replica-exchange method (REM)

KW - Simulated tempering (ST)

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U2 - 10.1016/j.cpc.2015.08.020

DO - 10.1016/j.cpc.2015.08.020

M3 - Article

AN - SCOPUS:84942986563

VL - 197

SP - 128

EP - 135

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

ER -