Abstract
For the Ising model on a bcc lattice we analyze the ground states associated with different interfaces and discuss some consequences on the roughening transition.
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References
C. Rottman and M. Wortis,Phys. Rep. 103:59 (1984).
H. van Beijeren and I. Nolden, The roughening transition, to be published.
D. B. Abraham, Surface structures and phase transitions-Exact results, in Phase Transitions and Critical Phenomena, Vol. 10, C. Domb and J. L. Lebowitz, eds. (Academic Press, London).
S. Balibar and B. Castaing, Helium: Solid-liquid interfaces,Surf. Sci. Rep. 5:87 (1985).
H. van Beijeren,Phys. Rev. Lett. 38:993 (1977).
H. W. J. Blöte and H. J. Hilhorst,J. Phys. A 15:L631 (1982).
B. Nienhuis, H. J. Hilhorst, and H. W. J. Blöte,J. Phys. A 17:3559 (1984).
R. L. Dobrushin, R. Kotecký, and S. B. Shlosman, in preparation.
R. L. Dobrushin and S. B. Shlosman,Sov. Sci. Rev. C 5:54 (1985).
R. Kotecký and S. Miracle-Sole,Phys. Rev. B 34:2049 (1986).
R. Kotecký and S. Miracle-Sole, inVIIIth International Congress on Mathematical Physics, R. Séneor and M. Mebkhout, eds. (World Scientific, Singapore).
Ya. G. Sinai,Theory of Phase Transitions: Rigorous Results (Pergamon, New York, 1982).
R. Kotecký,Phys. Rev. B 31:3088 (1985).
S. Pirogov and Ya. G. Sinaï,Teor. Mat. Fiz. 25:1185 (1975);26:39 (1976).
P. Holický, R. Kotecký, and M. Zahradník, Rigid interfaces for lattice models at low temperatures, Preprint, Marseille (1986).
J. R. Banavar, D. Jasnow, and D. P. Landau,Phys. Rev. B 20:3820 (1979).
R. L. Dobrushin,Theory Prob. Appl. 17:582 (1972).
H. van Beijeren,Commun. Math. Phys. 40:1 (1975).
J. Fröhlich, C. E. Pfister, and T. Spencer, inStochastic Processes in Quantum Theory and Statistical Physics, S. Albeverio, Ph. Combe, and M. Sirugue-Collin, eds. (Lecture Notes in Physics, Vol. 173, Springer, Berlin, 1982), p. 169.
J. Bricmont, J. R. Fontaine, and J. L. Lebowitz,J. Stat. Phys. 29:193 (1982).
J. L. Lebowitz,Commun. Math. Phys. 35:87 (1974).
J. Bricmont, A. El Mellouki, and J. Fröhlich,J. Stat. Phys. 42:743 (1986).
G. Gallavotti,Commun. Math. Phys. 27:103 (1972).
C. Jayaprakash, W. F. Saam, and S. Teitel,Phys. Rev. Lett. 50:2017 (1983).
C. Jayaprakash and W. F. Saam,Phys. Rev. B 30:3916 (1984).
J. Bricmont, J. L. Lebowitz, C. E. Pfister, and E. Olivieri,Commun. Math. Phys. 66:1 (1979); J. Bricmont, J. L. Lebowitz, and C. E. Pfister,Commun. Math. Phys. 66:21 (1979);69:267 (1979).
E. H. Lieb and F. Y. Wu, inPhase Transitions and Critical Phenomena, Vol. 1, C. Domb and M. S. Green, eds. (Academic Press, London, 1972).
J. B. Sutherland, C. N. Yang, and C. P. Yang,Phys. Rev. Lett. 19:588 (1967).
A. F. Andreev,Zh. Eksp. Teor. Fiz. 80:2042 (1981) [Sov. Phys. JETP 53:1063 (1982)].
J. Miekisz, Classical lattice gas model with a unique nondegenerate but unstable periodic ground state configuration, Preprint.
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Kotecký, R., Miracle-Sole, S. Roughening transition for the Ising model on a BCC lattice. A case in the theory of ground states. J Stat Phys 47, 773–799 (1987). https://doi.org/10.1007/BF01206158
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DOI: https://doi.org/10.1007/BF01206158