Abstract
For the 3-dimensional Ising model with long-range interaction, Gibbs states are constructed that are small perturbations of non-translation-invariant ground states. These ground states are in one-to-one correspondence with the set of all rational planes.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Ya. G. Sinai,Theory of Phase Transitions. Rigorous Results (Acad. Kiado, Budapest, 1982).
S. E. Burkov,J. Phys. (Paris) 46:317–327 (1985).
R. L. Dobrushin,Teor. Veroyat. Primenenie 17(4):619–639 (1972).
M. Aizenman,Commun. Math. Phys. 73:83–94 (1980).
Y. Higuchi,Random Fields, Colloquis Math. Soc. Janos Bolyai 271:517–534 (1981).
R. L. Dobrushin and B. B. Shlosman,Sov. Sci. Rev. Ser. C 5 (1985).
R. L. Dobrushin,Teor. Mat. Fiz. 12(1):115–134 (1972).
V. A. Malyshev,Uspekhi Mat. Nauk 50(3):3–53 (1970).
E. I. Dinaburg and Ya. G. Sinai, inInternational Symposium on Selected Topics in Statistical Mechanics (Dubna, 1984, Vol. 1, pp. 255–289 [in Russian].
J. Bricmont, K. Kuroda, and J. L. Lebowitz,Commun. Math. Phys. 101:501–538 (1985).
A. E. Mazel,Teor. Mat. Fiz. 68(1):128–140;68(2):287–300 (1986).
R. A. Minlos and Ya. G. Sinai,Trudy Mosk. Mat. Obshch. 17:213–242 (1967).
H. van Beijeren,Commun. Math. Phys. 40:1–7 (1975).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kerimov, A. Interface sharpness in the Ising model with long-range interaction. J Stat Phys 52, 69–98 (1988). https://doi.org/10.1007/BF01016405
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01016405