Abstract
Two models of self-avoiding surfaces on the cubic lattice are studied by Monte Carlo simulations. Both the first model with fluctuating boundary and the second one with a fixed boundary are found to belong to the universality class of branched polymers. The algorithms as well as the methods used to extract the critical exponents are described in detail. The results are compared to other recent estimates in the literature.
Similar content being viewed by others
References
R. Balian, J. M. Drouffe, and C. Itzykson,Phys. Rev. D 11:2104 (1975).
A. Polyakov,Phys. Lett. 103B:207 (1981).
P. G. de Gennes,Rev. Mod. Phys. 57:827 (1985).
H. J. Leamy, G. H. Gilmer, and K. A. Jackson, inSurface Physics of Crystalline Materials, J. M. Blakely, ed. (Academic Press, New York, 1976).
P. G. de Gennes,Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, New York, 1979).
P. G. de Gennes,Phys. Lett. 38A:339 (1972); T. C. Lubensky and J. Isaacson,Phys. Rev. A 20:2130 (1979).
Y. Kantor, M. Kardar, and D. R. Nelson,Phys. Rev. Lett. 57:791 (1986), and Harvard preprint.
M. E. Cates,Phys. Lett. 161B:363 (1985).
B. Widom,J. Phys. Chem. 88:6508 (1984);J. Chem. Phys. 84:6943 (1986).
T. Hofsaess and H. Kleinert,J. Chem. Phys. 86:3565 (1987).
W. Nelfrich,Z. Naturforsch. B 103:67 (1975).
U. Glaus,Phys. Rev. Lett. 56:1996 (1986).
U. Glaus and T. L. Einstein,J. Phys. A 20:L105 (1987).
J. Froehlich, inApplications of Field Theory to Statistical Mechanics, L. Garrido, ed. (Lecture Notes in Physics, Vol. 216, Springer, Berlin, 1985).
H. Tasaki and T. Hara,Phys. Lett. 112A:115 (1985).
A. Maritan and A. Stella,Phys. Rev. Lett. 53:123 (1984).
T. Sterling and J. Greensite,Phys. Lett. 121B:345 (1983).
B. Baumann and B. Berg,Phys. Lett. 164B:131 (1985).
M. Karowski,J. Phys. A 19:3375 (1986).
B. Berg and A. Billoire,Phys. Lett. 139B:297 (1984); R. Schrader,J. Stat. Phys. 40:533 (1985); M. Karowski and H. J. Thun,Phys. Rev. Lett. 54:2556 (1985).
J. M. Hammersley,Proc. Camb. Phil. Soc. 57:516 (1961).
B. Durhuus, J. Froehlich, and T. Jonsson,Nucl. Phys. B 225:185 (1983).
A. Bovier, J. Froehlich, and U. Glaus, inCritical Phenomena, Random Systems and Gauge Theories (Les Houches, Sesion XLIII), K. Osterwalder and R. Stora, eds. (Elsevier, Amsterdam, 1986).
B. Durhuus, J. Froehlich, and T. Jonsson,Nucl. Phys. B 240:453 (1984).
J. M. Drouffe, G. Parisi, and N. Sourlas,Nucl. Phys. B 161:397 (1980).
B. B. Mandelbrot,Fractals: Form Chance and Dimension (Freeman, San Francisco, 1977);The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
G. Parisi,Phys. Lett. 81B:357 (1979).
K. Symanzik, Euclidean quantum field theory, inLocal Quantum Theory, R. Jost, ed. (Academic Press, New York, 1969); D. Brydges, J. Froehlich, and T. Spencer,Commun. Math. Phys. 83:123 (1982).
D. B. Abraham, J. T. Chayes, and L. Chayes,Commun. Math. Phys. 96:439 (1984).
S. Caracciolo and U. Glaus,J. Stat. Phys. 41:95 (1985).
A. Berretti and A. Sokal,J. Stat. Phys. 40:483 (1985).
G. Parisi and N. Sourlas,Phys. Rev. Lett. 46:871 (1981).
S. Redner,J. Phys. A 18:L723 (1985),19:3199 (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Glaus, U. Monte Carlo study of self-avoiding surfaces. J Stat Phys 50, 1141–1166 (1988). https://doi.org/10.1007/BF01019158
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01019158