GRAND CANONICAL SIMULATIONS OF HARD-DISK SYSTEMS BY SIMULATED TEMPERING

Gunter Döge (), Klaus Mecke (), Jesper Møller (), Dietrich Stoyan () and Rasmus P. Waagepetersen ()
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Gunter Döge: Institut für Stochastik, TU Bergakademie Freiberg, D-09596 Freiberg, Germany
Klaus Mecke: Max-Planck-Institut für Metallforschung, D-70569 Stuttgart, Germany
Jesper Møller: Department of Mathematical Sciences, Aalborg University, DK-9220 Aalborg Ø, Denmark
Dietrich Stoyan: Institut für Stochastik, TU Bergakademie Freiberg, D-09596 Freiberg, Germany
Rasmus P. Waagepetersen: Department of Mathematical Sciences, Aalborg University, DK-9220 Aalborg Ø, Denmark

International Journal of Modern Physics C (IJMPC), 2004, vol. 15, issue 01, 129-147

Abstract: The melting transition of hard disks in two dimensions is still an unsolved problem and improved simulation algorithms may be helpful for its investigation. We suggest the application of simulating tempering for grand canonical hard-disk systems as an efficient alternative to the commonly-used Monte Carlo algorithms for canonical systems. This approach allows the direct study of the packing fraction as a function of the chemical potential even in the vicinity of the melting transition. Furthermore, estimates of several spatial characteristics including pair correlation function are studied in order to test the accuracy of the method and to analyze the melting transition in hard-disk systems. Our results seem to show that there is a weak first-order phase transition.

Keywords: Hard-disk model; phase transition; Metropolis Hastings; Simulated Tempering (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0129183104005565

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