Abstract
Improved hull walking algorithms for two-dimensional percolation are proposed. In these algorithms a walker explores the external perimeter of percolation clusters. With our modifications very large systems (sizeL) can be studied with finite and small memory requirement and in computation time τ∼L 7/4. Applications in determining spanning probabilities, continuum percolation, and percolation with nonuniform occupation probability are pointed out.
Similar content being viewed by others
References
D. Stauffer and A. Aharony,Introduction to Percolation Theory (Taylor and Francis, London, 1992).
R. H. Swendsen and J. S. Wang,Phys. Rev. Lett. 58:86 (1987); J. S. Wang and R. H. Swendsen,Physica A 167:565 (1990).
S. A. Trugman,Phys. Rev. B 27:7539 (1983).
J. Hoshen and R. Kopelman,Phys. Rev. B 14:3428 (1976).
R. M. Ziff, P. T. Cummings, and G. Stell,J. Phys. A 17:3009 (1984).
G. E. Lautenbaugh, Jr., and R. Smedley,C through DESIGN (Franklin, Beedle and Associates, Wilsonville, Oregon, 1988).
R. F. Voss,J. Phys. A 17:L373 (1984); T. Grossman and A. Aharony,J. Phys. A 19:L745 (1986); R. M. Ziff,Phys. Rev. Lett. 56:545 (1986).
H. Saleur and B. Duplatier,Phys. Rev. Lett. 58:2325 (1987); A. Bunde and J. F. Gouyet,J. Phys. A 18:L285 (1985).
B. Sapoval, M. Rosso, and J. F. Gouyet,J. Phys. Lett. (Paris)46:L149 (1985).
P. Grassberger,J. Phys. A 25:5475 (1992).
R. M. Ziff,Phys. Rev. Lett. 69:2670 (1992).
G. M. Adel'son-Vel'skii and E. M. Landis,Dokl. Akad. Nauk SSSR 146:263 (1962) [Sov. Math. 3:1259 (1962)]; D. E. Knuth,Sorting and Searching (Addison-Wesley, Reading, Massachusetts, 1973).
R. Sedgewick,Algorithms in C (Addison-Wesley, Reading, Massachusetts, 1990).
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,Numerical Recipes in C, 2nd ed. (Cambridge University Press, Cambridge, 1992), pp. 300–304.
M. Rosso,J. Phys. A 22:L131 (1989).
R. M. Ziff and B. Sapoval,J. Phys. A 19:L1169 (1986).
M. Rosso, J. F. Gouyet, and B. Sapoval,Phys. Rev. B 32:6053 (1986).
D. Wilkinson and J. F. Willemsen,J. Phys. A 16:3365 (1983); D. Wilkinson and M. Barsony,J. Phys. A 17:L129 (1984).
Author information
Authors and Affiliations
Additional information
Communicated by D. Stauffer
Rights and permissions
About this article
Cite this article
Vollmayr, H. Cluster hull algorithms for large systems with small memory requirement. J Stat Phys 74, 919–927 (1994). https://doi.org/10.1007/BF02188585
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02188585