Optimising the parameters of the Gibbs Ensemble Monte Carlo simulation of phase separation: the role of multiple relaxation times

ABSTRACT

We address the problem of how to choose the parameters of a Gibbs Ensemble Monte Carlo (GEMC) simulation of phase separation optimally through a systematic study of the autocorrelation functions of density fluctuation in a particular example. In this model the particles interact via a square well potential. Values of the temperature as well as the range of the square well potential are varied. We find that the normalised autocorrelation function is described accurately over a very large time scale as a linear combination of an exponential function with a time scale τ₂ and a stretched exponential function with a time scale τ₁ and an exponent α. Dependence of α, τ₁ and τ₂ on the temperature, the parameters of the GEMC algorithm and the range of the square well potential is investigated and interpreted. We use the insight thus obtained and the generality of some aspects of these results to construct the route to optimisation of the parameters of a GEMC simulation in a somewhat more generic situation involving a single-component phase separation.

KEYWORDS:

• Markov chain
• Monte Carlo simulation
• Gibbs Ensemble method
• phase separation
• density auto-correlation function

Acknowledgements

The parallel computing facilities used for this work have been provided to the School of Physical Sciences, Jawaharlal Nehru University by the Department of Science and Technology, Government of India, under its FIST-I and FIST-II programmes and also under its PURSE programme. B.K. acknowledges financial support from the University Grants Commission, India. The authors also wish to acknowledge the computational facilities provided by the School of Computational and Integrative Sciences, Jawaharlal Nehru University, where some of the calculations were performed.

Disclosure statement

No potential conflict of interest was reported by the author(s).