Journal of Statistical Physics

, Volume 74, Issue 3–4, pp 909–917 | Cite as

Two-dimensional lattice tree exponents and amplitudes: Simulation algorithms versus series

  • N. J. A. P. Gonçalves


We use a local Monte Carlo algorithm to simulate lattice trees in two dimensions for the site and bond problem. We investigate the properties of radius of gyration, perimeter-to-site ratio, and vertex degree in a tree, adding some new results in the site problem, compare our results on their noncritical properties with those obtained from earlier reversible and slightly nonreversible algorithms, and combine our determinations with new exact series expansion data. On the controversy surrounding the possible lack of universality for the first confluent singularity for the gyration radius, we feel that conclusions must be guarded.

Key Words

Lattice trees Monte Carlo radius perimeter corrections to scaling 


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  1. 1.
    Adler, J., Moshe, M., and Privman, V.,Phys. Rev. B 26:1411 (1982); J. Adler, I. Chang, and S. Shapira,Int. J. Mod. Phys. C 4 (1993).CrossRefGoogle Scholar
  2. 2.
    B. Derrida and L. DeSeze,J. Phys. (Paris)43:475 (1982).Google Scholar
  3. 3.
    J. A. M. S. Duarte,J. Phys. A: Math. Gen. 19:1979 (1986).CrossRefGoogle Scholar
  4. 4.
    J. A. M. S. Duarte,Portugal. Phys. 12:99 (1981).Google Scholar
  5. 5.
    J. A. M. S. Cadilhe and A. M. R. Cadilhe,J. Stat. Phys. 56:951 (1989).CrossRefGoogle Scholar
  6. 6.
    J. A. M. S. Duarte and H. J. Ruskin,J. Phys. (Paris)42:1585 (1981).Google Scholar
  7. 7.
    A. J. Guttmann,J. Phys. A: Math. Gen. 11:949 (1982).CrossRefGoogle Scholar
  8. 8.
    A. J. Guttmann and D. S. Gaunt,J. Phys. A: Math. Gen. 11:949 (1978).CrossRefGoogle Scholar
  9. 9.
    T. Ishinabe,J. Phys. A: Math. Gen. 22:4419 (1989).CrossRefGoogle Scholar
  10. 10.
    E. J. Janse van Rensburg and N. Madras,J. Phys. A: Math. Gen. 25:303 (1992).CrossRefGoogle Scholar
  11. 11.
    J. Kertész,J. Phys. A: Math. Gen. 19:599 (1986).CrossRefGoogle Scholar
  12. 12.
    T. Lubensky and J. Isaacson,Phys. Rev. A 20:2130 (1979).CrossRefGoogle Scholar
  13. 13.
    A. Margolina, H. Nakanishi, D. Stauffer, and H. E. Stanley,J. Phys. A: Math. Gen. 17:1683 (1984).CrossRefGoogle Scholar
  14. 14.
    V. Privman and M. E. Fisher,J. Phys. A: Math. Gen. 16:L295 (1983).CrossRefGoogle Scholar
  15. 15.
    W. A. Seitz and D. J. Klein,J. Chem. Phys. 75:5190 (1981).CrossRefGoogle Scholar
  16. 16.
    M. F. Sykes, D. S. Gaunt, and M. Glen,J. Phys. A: Math. Gen. 14:287 (1981).CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • N. J. A. P. Gonçalves
    • 1
  1. 1.Department of Pure and Applied PhysicsUniversity of SalfordSalfordEngland

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