Abstract
Under intuitively reasonable assumptions it is shown that in two dimensions different phases cannot exist locally. In three dimensions we discuss the possibility of local coexistence of districts with different magnetization for the Heisenberg ferromagnet and show that an interaction that breaks rotational invariance is necessary for this phenomenon.
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References
Ch. Kittel,Introduction to Solid State Physics (New York, 1967) [Einführung in die Festkörperphysik (Oldenburg, München, 1969)].
L. D. Landau, E. M. Lifschitz, and L. P. Pitajewski,Lehrbuch der theoretischen Physik IX (Akademie Verlag, Berlin, 1980).
N. D. Mermin and H. Wagner,Phys. Rev. Lett. 17:1133 (1966).
C. A. Bonato, J. F. Perez, and A. Klein, “The Mermin-Wagner Phenomenon and Cluster Properties,” preprint, Univ. de Sao Paulo (1981).
H. Araki and P. D. F. Jon,Commun. Math. Phys. 35:1 (1974).
J. Fröhlich and C. Pfister,Commun. Math. Phys. 81:277 (1981).
H. Kunz and C. E. Pfister,Commun. Math. Phys. 46:245 (1976).
G. Gallavotti,Commun. Math. Phys. 27:103 (1972).
A. Messager and S. Miracle Sole,J. Stat. Phys. 17:245 (1977).
R. L. Dobrushin,Theory Probab. Its Appl. 18:253 (1973).
H. Beijeren,Commun. Math. Phys. 40:1 (1975).
W. Thirring,Lehrbuch der Mathematischen Physik IV (Springer, Wien, 1980).
O. Bratteli and D. W. Robinson,Operator Algebras and Quantum Statistical Mechanics II (Springer, New York, 1981).
H. Araki,Commun. Math. Phys. 14:120 (1969).
H. Narnhofer, Thermodynamical Phases and Surface Effects, preprint (1981).
J. Fröhlich, C. E. Pfister, and T. Spencer, On the Statistical Mechanics of Surfaces, preprint IHES (1982).
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Narnhofer, H. Local coexistence of different phases. J Stat Phys 29, 761–771 (1982). https://doi.org/10.1007/BF01011789
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DOI: https://doi.org/10.1007/BF01011789