Abstract
We derive nonperturbatively — within the meanfield version of the Landau-Ginzburg-Wilson theory — the expressions for the constrained order parameter, for the coefficient of surface stiffness, and for the effective interface potential of a fluctuating interface in the presence of a flat substrate. The derived expressions display the typical dependence on the distancel between the interface and the substrate; the exponentially decaying contributions are multiplied by polynomials inl. We show that the expressions for the coefficient of surface stiffness and for the effective interface potential have identical form as those proposed recently by Jin and Fisher (Phys. Rev.B 47, 7365 (1993)).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Dietrich, inPhase Transitions and Critical Phenomena, ed. by C. Domb and J. Lebowitz (Academic, London, 1988), Vol.12, p. 1.
M. E. Fisher, inStatistical Mechanics of Membranes and Surfaces, ed. by D. Nelson, T. Piran, and S. Weinberg (World Scientific, Singapore, 1989).
E. Brézin, B. I. Halperin, and S. Leibler, Phys. Rev. Lett.50, 1387 (1983); and J. Phys. (Paris),44, 775 (1983).
D. S. Fisher and D. A. Huse, Phys. Rev.B 32, 247 (1985).
E. H. Hauge and K. Olaussen, Phys. Rev.B 32, 4766 (1985).
R. Lipowsky, and M. E. Fisher. Phys. Rev. lett.57, 2411 (1986).
K. Binder, D. P. Landau, and D. M. Kroll, Phys. Rev. Lett.56, 2272 (1986).
K. Binder and D. P. Landau, Phys. Rev.B 37, 1745, (1988).
K. Binder, D. P. Landau, and S. Weinsleban, Phys. Rev.B 40, 6971 (1989).
G. Gompper and D. M. Kroll, Phys. Rev.B 37, 3821 (1988).
G. Gompper, D. Kroll, and R. Lipowsky, Phys. Rev.B 42, 961 (1990).
A. O. Parry, R. Evans, and K. Binder, Phys. Rev.B 43, 1153 (1991).
M. E. Fisher and A. J. Jin, Phys. Rev.B 44, 1430 (1991).
M. E. Fisher and A. J. Jin, Phys. Rev. Lett.69, 792 (1992).
A. J. Jin and M. E. Fisher, Phys. Rev.B 47, 7365 (1993).
M. E. Fisher, A. J. Jin, and A. O. Parry, Ber. Bunsenges. Phys. Chem.98, 357 (1994).
A. J. Jin and M. E. Fisher, Phys. Rev.B, 48, 2642 (1993).
A. O. Parry and C. J. Boulter, J. Phys. A27, L351 (1994).
H. W. Diehl, D. M. Kroll, and H. Wagner, Z. Phys.B, 36, 329 (1980).
R. Lipowsky, D. M. Kroll, and R. Zia, Phys. Rev.B 27, 4499 (1983). Here, for the first time, a hint is made that the capillary wave Hamiltonian may contain thel-dependent surface stiffness coefficient.
R. Lipowsky, Z. Phys.B 55, 345 (1984).
S. C. Liu and M. J. Lowe, J. Phys. A16, 347 (1983).
M. P. A. Fisher and M. Wortis, Phys. Rev. B29, 6252 (1984).
R. K. R. Zia, Nucl. Phys.B 251 [FS13], 676 (1985).
G. Gompper and S. Zschocke, Europhys. Lett.16, 731 (1991); Phys. Rev. A46, 4836 (1992); G. Gompper and M. Kraus, Phys. Rev.E 47, 4289, 4301 (1993).
E. M. Blokhuis and D. Bedeaux, J. Chem. Phys.95, 6986 (1991); Physica A184, 42 (1992); Mol. Phys.80, 705 (1993).
V. Romero-Rochiń, C. Varea, and A. Robledo, Physica A184, 367 (1992); Phys. Rev. A44, 8417 (1991); inLectures on Thermodynamics and Statistical Mechanics, ed. by M. L. de Haro and C. Varea (World Scientific, Singapore, 1991), p.10; Physica A177, 474 (1991).
J. B. Keller and G. J. Merchant, J. Stat. Phys.63, 1039 (1991).
J. H. Pérez-López and J. E. Puig, Physica A172, 309 (1991).
S. Dietrich and M. Napiórkowski, Physica A177, 437 (1991); M. Napiórkowski and S. Dietrich, Z. Phys. B89, 263 (1992); Phys. Rev. E47, 1836 (1993); M. Napiórkowski, Ber. Bunsenges. Phys. Chem.98, 352 (1994).
The termw 30 exp (−3p β l) is missing in Refs. [14] and [15]; its presence has no influence on the outcome of the renormalization group analysis.
Author information
Authors and Affiliations
Additional information
Dedicated to Herbert Wagner on the occasion of his 60th birthday