Skip to main content
SpringerLink
Log in
Book cover

Statistical Physics and Spatial Statistics pp 379–393Cite as

Grand Canonical Simulations ofHard-Disk Systems by Simulated Tempering

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Physics ((LNP,volume 554))

Abstract

For the simulation of hard core Gibbs point processes simulated tempering is shown to be an efficient alternative to commonly used Markov chain Monte Carlo algorithms. The behaviour of the area fraction and various spatial characteristics of the hard core process is studied using simulated samples.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alder, B.J., T.E. Wainwright (1957): ‘Phase transition of a hard sphere system’, J. Chem. Phys. 27, pp. 1208–1209

    Article  ADS  Google Scholar 

  2. Alder, B.J., T.E. Wainwright (1962): ‘Phase transition in elastic disks’, Phys. Rev. 127, pp. 359–361

    Article  ADS  Google Scholar 

  3. Allen, M.P., D.J. Tildesley (1987): Computer Simulation of Liquids (Oxford University Press, Oxford)

    MATH  Google Scholar 

  4. Bagchi, K., H.C. Andersen, W. Swope (1996): ‘Computer simulation study of the melting transition in two dimensions’, Phys. Rev. Lett. 76, pp. 255–258

    Article  ADS  Google Scholar 

  5. Binder, K. (Ed.) (1995): The Monte Carlo Method in Condensed Matter Physics (Topics in Applied Physics Vol. 71, Springer, Berlin)

    Google Scholar 

  6. Ciccotti, G., D. Frenkel, I.R. McDonald (Eds.) (1987): Simulation of liquids and solids. Molecular Dynamics and Monte Carlo Methods in Statistical Mechanics (North-Holland, Amsterdam)

    Google Scholar 

  7. Fernàndez, J.F., J.J. Alonso, E. Stankiewicz (1995): ‘One-stage continuous melting transition in two dimensions’, Phys. Rev. Lett. 75, pp. 3477–3480

    Article  ADS  Google Scholar 

  8. Frenkel, D., B. Smit (1996): Understanding molecular simulation. From algorithms to applications (Academic Press, San Diego)

    MATH  Google Scholar 

  9. Geyer, C.J., J. Møller (1994): ‘Simulation procedures and likelihood inference for spatial point processes’, Scand. J. Statist. 21, pp. 359–373

    MATH  MathSciNet  Google Scholar 

  10. Geyer, C.J., E.A. Thompson (1995): ‘Annealing Markov chain Monte Carlo with applications to pedigree analysis’, J. Am. Statist. Ass. 90, pp. 909–920

    Article  MATH  Google Scholar 

  11. Geyer, C.J. (1999): ‘Likelihood inference for spatial point processes’. In: Stochastic Geometry: Likelihood and Computations, ed. by O.E. Barndor.-Nielsen, W.S. Kendall, M.N.M. van Lieshout (Chapman and Hall/CRC, London) pp. 79–140

    Google Scholar 

  12. Hansen, J.-P., I.R. McDonald (1986): Theory of Simple Liquids (Academic Press, London)

    Google Scholar 

  13. Hoover, W.G., F.H. Ree (1969): ‘Melting Transition and Communal Entropy for Hard Spheres’, J. Chem. Phys. 49, pp. 3609–3617

    Article  ADS  Google Scholar 

  14. Jaster, A. (1999): ‘An improved Metropolis algorithm for hard core systems’, condmat/9810274 (21. Oct. 1998); Physica A 264, p. 134

    Google Scholar 

  15. Kosterlitz, J.M., D.J. Thouless (1973): ‘Ordering metastability and phase transformation in two-dimensional systems’, J. Phys. C 6, pp. 1181–1203; Kosterlitz, J.M. (1974): ‘The critical properties of the two-dimensional xy model’, J. Phys. C 7, pp. 1046-1060; Berenzinskii, V.L. (1972): ‘Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II.Quantum systems’, Sov. Phys. JETP 34, pp. 610-616

    Article  ADS  Google Scholar 

  16. Lee, J., K.J. Strandburg (1992): ‘First-order melting transition of the hard-disk system’, Phys. Rev. B 46, p. 11190–11193

    Article  ADS  Google Scholar 

  17. Marcus, A.H., S.A. Rice (1996): ‘Observations of First-Order Liquid-to-Hexatic and Hexatic-to-Solid Phase Transitions in a Confined Colloid Suspension’, Phys. Rev. Lett. 77, pp. 2577–2580

    Article  ADS  Google Scholar 

  18. Marinari, E., G. Parisi (1992): ‘Simulated tempering: A new Monte Carlo scheme’, Europhysics Letters 19, pp. 451–458

    Article  ADS  Google Scholar 

  19. Mase, S., J. Møller, D. Stoyan, R.P. Waagepetersen, G. Döge (1999): ‘Packing Densities and Simulated Tempering for Hard Core Gibbs Point Processes’, (submitted 1999)

    Google Scholar 

  20. Metropolis, N., A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller (1953): ‘Equation of state calculations by fast computing machines’, J. Chemical Physics 21, pp. 1087–1092

    Article  ADS  Google Scholar 

  21. Møller, J. (1999): ‘Markov chain Monte Carlo and spatial point processes’. In:Stochastic Geometry: Likelihood and Computations, ed. by O.E. Barndor.-Nielsen, W.S. Kendall, M.N.M. van Lieshout (Chapman and Hall/CRC, London) pp. 141–172

    Google Scholar 

  22. Nelson, D.R., B.I. Halperin (1979): ‘Dislocation-mediated melting in two dimensions’, Phys. Rev. B 19, pp. 2457–2484; Young, A.P. (1979): ‘Melting and the vector Coulomb gas in two dimensions’, Phys. Rev. B 19, p. 1855

    Article  ADS  Google Scholar 

  23. Schmidt, M. (1997): Freezing in confined geometry. PhD-thesis, Düsseldorf (Shaker Verlag, Aachen)

    Google Scholar 

  24. Stoyan, D., W.S. Kendall, J. Mecke (1995): Stochastic Geometry and its Applications, 2nd edn. (Wiley & Sons, New York)

    MATH  Google Scholar 

  25. K.J. Strandburg (1988): ‘Two-dimensional melting’, Rev. Mod. Phys. 60, pp. 161–207

    Article  ADS  Google Scholar 

  26. Swope, W.C., H.C. Andersen (1992): ‘Thermodynamics, statistical thermodynamics, and computer simulation of crystals with vacancies and interstitials’, Phys. Rev. A 46, pp. 4539–4548; ‘A computer simulation method for the calculation of liquids and solids using the bicanonical ensemble’, J. Chem. Phys. 102, pp. 2851-2863 (1995)

    Article  ADS  Google Scholar 

  27. Truskett, T.M., S. Torquato, S. Sastry, P.G. Debenetti, F.H. Stillinger (1998): ‘A structural precursor to freezing in the hard-disk and hard-sphere systems’, Phys. Rev. E 58, pp. 3083–3088

    Article  ADS  Google Scholar 

  28. Weber, H. D. Marx (1994): ‘Two-dimensional melting approached via finite-size scaling of bond-orientational order’, Europhys. Lett. 27, pp. 593–598

    Article  ADS  Google Scholar 

  29. Weber, H., D. Marx, K. Binder (1995): ‘Melting transition in two dimensions: A finite-size scaling analysis of bond-orientational order in hard disks’, Phys. Rev. B 51, pp. 14636–14651

    Article  ADS  Google Scholar 

  30. Zollweg, J.A., G.V. Chester, P.W. Leung (1992): ‘Melting in two dimensions’, Phys. Rev. B 46, pp. 11186–11189

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Stochastics, Freiberg University of Mining and Technology, Bernhard-von-Cotta-Str. 2, D-09596, Freiberg, Germany

    Gunter Döge

Authors
  1. Gunter Döge
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fachbereich Physik, Bergische Universität Wuppertal, 42097, Wuppertal, Germany

    Klaus R. Mecke

  2. Institut für Stochastik, TU Bergakademie Freiberg, 09596, Freiberg, Germany

    Dietrich Stoyan

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Döge, G. (2000). Grand Canonical Simulations ofHard-Disk Systems by Simulated Tempering. In: Mecke, K.R., Stoyan, D. (eds) Statistical Physics and Spatial Statistics. Lecture Notes in Physics, vol 554. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45043-2_14

Download citation

  • DOI: https://doi.org/10.1007/3-540-45043-2_14

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67750-5

  • Online ISBN: 978-3-540-45043-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation