Journal of Statistical Physics

, Volume 82, Issue 1–2, pp 155–181 | Cite as

Monte carlo study of the interacting self-avoiding walk model in three dimensions

  • M. C. Tesi
  • E. J. Janse van Rensburg
  • E. Orlandini
  • S. G. Whittington
Articles

Abstract

We consider self-avoiding walks on the simple cubic lattice in which neighboring pairs of vertices of the walk (not connected by an edge) have an associated pair-wise additive energy. If the associated force is attractive, then the walk can collapse from a coil to a compact ball. We describe two Monte Carlo algorithms which we used to investigate this collapse process, and the properties of the walk as a function of the energy or temperature. We report results about the thermodynamic and configurational properties of the walks and estimate the location of the collapse transition.

Key Words

Self-avoiding walks lattice models Markov chains Monte Carlo phase transitions 

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References

  1. 1.
    G. M. Torrie and J. P. Valleau,J. Comput. Phys. 23:187 (1977).ADSCrossRefGoogle Scholar
  2. 2.
    C. J. Geyer and E. A. Thompson, Preprint, University of Minnesota (1994).Google Scholar
  3. 3.
    S. T. Sun, I. Nishio, G. Swislow, and T. Tanaka,J. Chem. Phys. 73:5971 (1980).ADSCrossRefGoogle Scholar
  4. 4.
    I. H. Park, J. H. Kim, and T. Chang,Macromolecules 25:7300 (1992).ADSCrossRefGoogle Scholar
  5. 5.
    S. F. Sun,J. Chem. Phys. 93:7508 (1990).ADSCrossRefGoogle Scholar
  6. 6.
    B. Nienhuis,J. Stat. Phys. 34:731 (1984).MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    A. Coniglio, N. Jan, I. Majid, and H. E. Stanley,Phys. Rev. B 35:3617 (1987); B. Duplantier and H. Saleur,Phys. Rev. Lett. 59:539 (1987); F. Seno and A. L. Stella,J. Phys. (Paris)49: 739 (1988).ADSCrossRefGoogle Scholar
  8. 8.
    P. G. de Gennes,J. Phys. Lett. (Paris)36:L55 (1975).ADSCrossRefGoogle Scholar
  9. 9.
    P. G. de Gennes,J. Phys. Lett. (Paris)39:L299 (1978).CrossRefGoogle Scholar
  10. 10.
    B. Duplantier,Europhys. Lett. 1:491 (1986;J. Chem. Phys. 86:4233 (1987).ADSCrossRefGoogle Scholar
  11. 11.
    A. L. Kholodenko and K. F. Freed,J. Chem. Phys. 80:900 (1984);J. Phys. A 17:L191 (1984).MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    A. Maritan, F. Seno, and A. L. Stella,Physica A 156:679 (1989).ADSCrossRefGoogle Scholar
  13. 13.
    H. Saleur,J. Stat. Phys. 45:419 (1986).ADSCrossRefGoogle Scholar
  14. 14.
    R. Finsy, M. Janssens, and A. Bellemans,J. Phys. A 8:L106 (1975).ADSCrossRefGoogle Scholar
  15. 15.
    D. C. Rapaport,J. Phys. A 9:1521 (1976).ADSCrossRefGoogle Scholar
  16. 16.
    T. Ishinabe,J. Phys. A 20:6435 (1985).ADSCrossRefGoogle Scholar
  17. 17.
    V. Privman,J. Phys. A 19:3287 (1987).ADSCrossRefGoogle Scholar
  18. 18.
    V. Privman and D. A. Kurtze,Macromolecules 19:2377 (1986).ADSCrossRefGoogle Scholar
  19. 19.
    J. Mazur and F. L. McCrackin,J. Chem. Phys. 49:648 (1968).ADSCrossRefGoogle Scholar
  20. 20.
    K. Kremer, A. Baumgartner, and K. Binder,J. Phys. A 15:2879 (1981).ADSCrossRefGoogle Scholar
  21. 21.
    I. Webman, J. L. Lebowitz, and M. H. Kalos,Macromolecules 14:1495 (1981).ADSCrossRefGoogle Scholar
  22. 22.
    H. Meirovitch and H. A. Lim,J. Chem. Phys. 92:5144 (1990).ADSCrossRefGoogle Scholar
  23. 23.
    J. M. Hammersley and D. C. Handscomb,Monte Carlo Methods (Methuen, London, 1964).MATHCrossRefGoogle Scholar
  24. 24.
    M. Lal,Mol. Phys. 17:57 (1969).ADSCrossRefGoogle Scholar
  25. 25.
    N. Madras and A. D. Sokal,J. Stat. Phys. 56:109 (1988).MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    J. P. Valleau, InProceedings of the International Symposium on Ludwig Boltzmann, G. Battimelli, M. G. Ianniello, and O. Kresten, eds. (1993).Google Scholar
  27. 27.
    B. A. Berg and T. Neuhaus,Phys. Rev. Lett. 68:9 (1992).ADSCrossRefGoogle Scholar
  28. 28.
    N. Madras and M. Piccioni,Importance sampling for families of distributions, Bernoulli (1994) submitted.Google Scholar
  29. 29.
    J. P. Valleau,J. Chem. Phys. 99:4718 (1993).ADSCrossRefGoogle Scholar
  30. 30.
    N. Madras and A. D. Sokal,J. Stat. Phys. 47:573 (1987).MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    A. D. Sokal,Monte Carlo methods for the self-avoiding walk, preprint (1994).Google Scholar
  32. 32.
    S. Caracciolo, A. Pelissetto, and A. D. Sokal,Phys. Rev. Lett. 72:179 (1994).MathSciNetADSMATHCrossRefGoogle Scholar
  33. 33.
    F. Yates,Sampling Methods for Censuses and Surveys (Griffin, 1960).Google Scholar
  34. 34.
    W. E. Deming,Some Theory of Sampling (Dover, New York, 1966).MATHGoogle Scholar
  35. 35.
    S. Caracciolo, A. Pelissetto, and A. D. Sokal,Monte Carlo methods using reweighting: some warnings, preprint (1994).Google Scholar
  36. 36.
    B. Li, N. Madras, and A. D. Sokal.Critical exponents, hyperscaling and universal amplitude ratios for two- and three-dimensional self-avoiding walks, preprint (1994).Google Scholar
  37. 37.
    P. Grassberger and R. HeggerSimulations of 3-dimensional Θ-Polymer, preprint (1994).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • M. C. Tesi
    • 1
  • E. J. Janse van Rensburg
    • 2
  • E. Orlandini
    • 3
  • S. G. Whittington
    • 1
  1. 1.Department of ChemistryUniversity of TorontoTorontoCanada
  2. 2.Department of MathematicsYork UniversityNorth YorkCanada
  3. 3.Theoretical PhysicsUniversity of OxfordOxfordUK

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