Abstract
The Ising square lattice with nearest-neighbor exchangeJ>0 and a free surface at which a boundary magnetic fieldH 1 acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surface steps are briefly discussed.
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References
D. E. Sullivan and M. M. Telo da Gama, inFluid Interfacial Phenomena, C. A. Croxton, ed. (Wiley, New York 1986).
S. Dietrich, inPhase Transitions and Critical Phenomena, Vol. XII, C. Domb and J. L. Lebowitz, eds. (Academic, New York, 1988), p. 1.
E. H. Hauge, inFundamental Problems in Statistical Physics VI, E. G. D. Cohen (North-Holland, Amsterdam, 1985), p. 65.
W. Selke, D. A. Huse, and D. M. Kroll,J. Phys. A 17:3019 (1984).
P. G. de Gennes,Rev. Mod. Phys. 55:825 (1985); M. E. Fisher,J. Chem. Soc. Faraday Trans.282:1569 (1986);J. Stat. Phys. 34:667 (1984).
E. Brézin, B. I. Halperin, and R. K. P. Zia,Phys. Rev. Lett. 50:1387 (1983).
R. Lipowsky, D. M. Kroll, and R. K. P. Zia,Phys. Rev. B 27:4499 (1983).
D. S. Fisher and D. A. Huse,Phys. Rev. B 32:247 (1985).
K. Binder, D. P. Landau, and D. M. Kroll,Phys. Rev. Lett. 56:2276 (1986).
R. Lipowsky and M. E. Fisher,Phys. Rev. B 36:2126 (1987);Phys. Rev. Lett. 57:2411 (1986).
E. Brézin and T. Halpin-Healey,Phys. Rev. Lett. 58:1220 (1987).
E. Brézin and T. Halpin-Healey,J. Phys. (Paris)48:757 (1987).
K. Binder and D. P. Landau,Phys. Rev. B 37:1745 (1988).
D. M. Kroll,J. Appl. Phys. 61:3595 (1988); G. Gompper and D. M. Kroll,Phys. Rev. B 37:529 (1988).
K. Binder, D. P. Landau, and S. Wansleben,Phys. Rev. B 40:6971 (1989).
A. D. Parry and R. Evans,Phys. Rev. B 39:12336 (1989).
T. Halpin-Healey,Phys. Rev. B 40 (1989).
D. B. Abraham,Phys. Rev. Lett. 44:1165 (1980).
D. B. Abraham, inPhase Transitions and Critical Phenomena, Vol. X, C. Domb and J. L. Lebowitz, eds. (Academic, New York, 1987), p. 1.
D. B. Abraham and D. A. Huse,Phys. Rev. B 38:7169 (1988).
D. B. Abraham and E. R. Smith,J. Stat. Phys. 43:621 (1986).
D. B. Abraham,J. Phys. A 21:1741 (1988).
S. T. Chui and J. D. Weeks,Phys. Rev. B 23:2438 (1981).
T. W. Burkhardt,J. Phys. A 14:L63 (1981).
D. M. Kroll,Z. Phys. B 41:345 (1981).
J. M. J. van Leeuwen and H. J. Hilhorst,Physica A 107:319 (1981).
V. Privman and N. M. Švrakic,Phys. Rev. B 37:3713 (1988).
D. M. Kroll and G. Gompper,Phys. Rev. B 39:433 (1989).
K. Binder, inPhase Transitions and Critical Phenomena, Vol. VIII, C. Domb and J. L. Lebowitz, eds. (Academic, New York, 1983), p. 1.
K. Binder and J. S. Wang,J. Stat. Phys. 55:87 (1989).
K. Binder and D. P. Landau,Phys. Rev. B 30:1477 (1984).
D. W. Heermann and R. C. Desai,Computer Phys. Commun. 50:536 (1988); R. C. Desai, D. W. Heermann, and K. Binder,J. Stat. Phys. 53:795 (1988).
E. V. Albano, K. Binder, D. W. Heermann, and W. Paul,Z. Phys. B 77:445 (1989).
E. V. Albano, K. Binder, D. W. Heermann, and W. Paul,Surf. Sci. 223:151 (1989).
E. V. Albano, K. Binder, D. W. Heermann, and W. Paul,J. Chem. Phys. 91:3700 (1989).
M. E. Fisher and H. Nakanishi,J. Chem. Phys. 75:5857 (1981); H. Nakanishi and M. E. Fisher,J. Chem. Phys. 78:3279 (1983).
M. E. Fisher,J. Phys. Soc. Japan Suppl. 26:87 (1969); see also G. G. Cabrera, R. Jullien, E. Brézin, and J. Zinn-Justin,J. Phys. (Paris)47:1305 (1986).
R. Lipowsky,Phys. Rev. B 32:173 (1985).
J. S. Wang, K. Binder, and J. L. Lebowitz,J. Stat. Phys. 56:783 (1989).
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Alexander von Humboldt-Fellow
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Albano, E.V., Binder, K., Heermann, D.W. et al. Critical wetting in the square Ising model with a boundary field. J Stat Phys 61, 161–178 (1990). https://doi.org/10.1007/BF01013958
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DOI: https://doi.org/10.1007/BF01013958