Abstract
We discuss the wetting of the interface between two ordered phases by the disordered one in the Potts model withq large. We argue that a “low-temperature” expansion can be used in this situation, with logq replacingβ. This model is analogous to the Blume-Capel model at low temperatures, which we use as an example to review the low-temperature expansions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. Selke, Interfacial adsorption in multi-state models, inStatic Critical Phenomena in Inhomogeneous Systems, A. Pekalski and J. Sznajd, eds. (Springer, 1984).
B. Derrida and M. Schick,J. Phys. A 19:1439 (1986).
K. Binder, Critical behavior at surfaces, inPhase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, 1983).
R. Pandit, M. Schick, and M. Wortis,Phys. Rev. B 26:5112 (1982).
P. Duxbury and J. Yeomans,J. Phys. A 18:L983 (1985); K. Armistead, J. Yeomans, and P. Duxbury,J. Phys. A 19:3165 (1986).
P. Upton and J. Yeomans, Layering transitions at an interface in the Blume-Capel model, Oxford University preprint.
J. Slawny, Low temperature properties of classical lattice systems: Phase transitions and phase diagrams, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, 1986); J. Slawny,J. Stat. Phys. 20:711 (1979).
M. E. Fisher and W. Selke,Phil. Trans. R. Soc. A 302:1 (1981).
S. Pirogov and Y. Sinai,Theor. Math. Phys. 25:1185 (1975);26:39 (1976); Y. Sinai,Theory of Phase Transitions, Rigorous Results (Pergamon Press, 1982).
J. Bricmont, A. El Mellouki, and J. Fröhlich,J. Stat. Phys. 42:743 (1986); J. Fröhlich and C. E. Pfister, The semi-infinite Ising model I and II,Commun. Math. Phys., to appear.
W. Selke, D. Huse, and D. Kroll,J. Phys. A 17:3019 (1984).
R. Israël,Convexity in the Theory of Lattice Gases (Princeton University Press, 1979).
S. Isakov,Commun. Math. Phys. 95:427 (1984).
R. Dobrushin,Theor. Prob. Appl. 17:582 (1972).
P. Holicky, R. Kotecki, and M. Zahradnik, Rigid interfaces, preprint (1986).
M. Aizenman,Commun. Math. Phys. 73:83 (1980).
Y. Higushi, inRandom Fields, Vol. 1, J. J. Fritz, J. L. Lebowitz, and D. Szasz, eds. (North-Holland, 1981), p. 517.
R. Dobrushin and S. Schlosman, inSoviet Science Reviews, Series C, Vol. 5.
J. Bricmont, J. L. Lebowitz, and C. Pfister,J. Stat. Phys. 26:313 (1981).
M. de Oliveira and R. Griffiths,Surf. Sci. 71:687 (1978).
R. Kotecki and S. Schlosman,Commun. Math. Phys. 83:493 (1982).
D. Martirosian,Commun. Math. Phys. 105:281 (1986).
J. Bricmont and J. Slawny, First order phase transitions and perturbation theory, inStatistical Mechanics and Field Theory: Mathematical Aspects, T. Dorlas, N. M. Hugenholtz, and M. Winnink, eds. (Springer-Verlag, 1986), p. 10.
Y. Goldschmidt,Phys. Rev. B 24:1374 (1981).
R. Lipowski, D. Kroll and R. Zia,Phys. Rev. B 27:4499 (1983); D. Abraham and E. Smith,Phys. Rev. B 26:1480 (1982); W. Selke, D. Huse, and D. Kroll,J. Phys. A 17:3019 (1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bricmont, J., Lebowitz, J.L. Wetting in Potts and Blume-Capel models. J Stat Phys 46, 1015–1029 (1987). https://doi.org/10.1007/BF01011154
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01011154