Abstract
The effect of collective modes on the otherwise local structure of Ising lattices is investigated by studying a number of exactly solvable models. First, the open one-dimensional Ising model serves to define sharp locality. This feature then remains upon extension to a Bethe lattice, despite the existence of a phase transition. But insertion of periodic boundary conditions creates a collective mode which breaks locality in a very specific fashion. A model interface is analyzed to show that even when locality is not broken, local uniformity can become untenable.
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References
J. K. Percus,J. Stat. Phys. 16:299 (1977).
C. Borzi, G. Ord, and J. K. Percus,J. Stat. Phys. 46:51 (1987).
M. Kac, inApplied Probability, L. A. MacColl, ed. (McGraw-Hill, New York, 1957); A. J. F. Siegert, inStatistical Physics (1962 Brandeis Lectures; Benjamin, New York, 1963).
S. K. Ma,Statistical Mechanics (World Scientific, Philadelphia, 1985).
J. K. Percus, Non-uniform fluids, inThe Liquid State of Matter, E. W. Montroll and J. L. Lebowitz, eds. (North-Holland, New York, 1982).
J. K. Percus,J. Math. Phys. 23:1162 (1982).
E. Müller-Hartman and J. Zittartz,Phys. Rev. Lett. 33:893 (1974).
H. A. Bethe,Proc. Roy. Soc. A 150:552 (1935).
L. Samaj,J. Phys. France 50:273 (1989).
J. K. Percus and M. Q. Zhang,Phys. Rev. B. 38:11737 (1988).
G. Ord, J. K. Percus, and M. Q. Zhang,Nucl. Phys. B 305:271 (1988).
D. Jasnow, B. B. Pant, T. Ohta,Phys. Rev. A 26:3532 (1982).
J. K. Percus,J. Chem. Phys. 81:452 (1984);J. Phys. Chem. 88:6499 (1984).
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Percus, J.K. Collective modes in Ising lattices. J Stat Phys 55, 1263–1277 (1989). https://doi.org/10.1007/BF01041086
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DOI: https://doi.org/10.1007/BF01041086