Abstract
The external potential needed to produce an arbitrary equilibrium density profile for a one-dimensional lattice gas with nearest neighbor interactions is solved exactly. The resulting sequence of direct correlation functions is shown to be of short range, and in the ferromagnetic case the even members alternate in sign at zero spin. The even Ursell distributions in this case likewise alternate in sign.
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References
K. S. Liu,J. Chem. Phys. 60:4226 (1974); K. S. Liu, M. H. Kalos, and G. V. Chester,Phys. Rev. A 10:303 (1974); J. K. Percus,J. Stat. Phys. 15:423 (1976).
E. H. Lieb and D. C. Mattis,Mathematical Physics in One Dimension, Academic Press, New York (1966).
J. K. Percus, inEquilibrium Theory of Classical Fluids, H. Frisch and J. L. Lebowitz, eds., Benjamin, New York (1964).
C. Thompson,Mathematical Statistical Mechanics, Macmillan, New York (1972).
H. S. Wall,Analytic Theory of Continued Fractions, Van Nostrand, New York (1948), p. 51.
N. Seto,Prog. Theor. Phys. 54:1881 (1975).
J. Groeneveld,Phys. Lett. 3:50 (1962).
J. Rosen, to be published.
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Supported in part by U.S. ERDA under contract E(11-1)-3077.
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Percus, J.K. One-dimensional Ising model in arbitrary external field. J Stat Phys 16, 299–309 (1977). https://doi.org/10.1007/BF01020384
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DOI: https://doi.org/10.1007/BF01020384