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General method to sample systems in the microcanonical ensemble using Monte Carlo simulations

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient simulation algorithms. Nevertheless, nature does not know about statistical ensembles and therefore it is desirable and a theoretical challenge to show how to perform numerical simulations in the microcanonical ensemble without the use of unphysical degrees of freedom. In this article, we present a straightforward applicable method based on the concepts of a configurational temperature estimator (Rugh Phys Rev Lett 78:772, 1997; Gutiérrez et al. J Phys A Math Theor 51:455003, 2018) and on stochastic dynamics, which is independent of the Monte Carlo update strategy, and can be implemented for both local update or cluster algorithms. We illustrate it by performing a numerical simulation of the two-dimensional XY-model, finding the equilibrium temperature of two spin subsystems initially at different temperatures when they are put into thermal contact.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data used to produce the different figures can be requested to the corresponding author if required.]

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Acknowledgements

This work was partially supported by Dicyt-USACH Grant No. 041831PA. A.R. acknowledges support from CONICYT + PAI / Convocatoria Nacional Subvención a la instalación en la Academia, convocatoria 2019 + Folio 77190042.

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Authors and Affiliations

  1. Departamento de Física, Facultad de Ciencia, Universidad de Santiago de Chile, Avda. Ecuador 3493, 9170124, Santiago, Chile

    G. Palma

  2. Escuela de Ingeniería, Universidad Central de Chile, 8330601, Santiago, Chile

    A. Riveros

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  1. G. Palma
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  2. A. Riveros
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Contributions

The idea for this study was proposed by GP, the elaboration of the method was carried out by both authors. The numerical results were obtained by AR. Both authors contributed to the data analysis, the discussions and the writing of the manuscript.

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Correspondence to A. Riveros.

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Palma, G., Riveros, A. General method to sample systems in the microcanonical ensemble using Monte Carlo simulations . Eur. Phys. J. B 94, 23 (2021). https://doi.org/10.1140/epjb/s10051-020-00022-6

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