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

Ryo Urano, Yuko Okamoto

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)128-135
Number of pages8
JournalComputer Physics Communications
Publication statusPublished - Dec 1 2015
Externally publishedYes


  • Differential equation
  • Gibbs sampling
  • Heat-bath method
  • Ising model
  • Monte Carlo (MC) simulation
  • Pseudo random numbers
  • Replica-exchange method (REM)
  • Simulated tempering (ST)

ASJC Scopus subject areas

  • Hardware and Architecture
  • General Physics and Astronomy


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