Abstract
Using the necessary and sufficient conditions in terms of the high-field series coefficients that the Yang-Lee theorem holds, we prove rigorously by counterexample that it cannot be extended to general noninteger dimension, when such models are defined by the “natural” analytic continuation.
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References
E. M. Fisher and D. S. Gaunt,Phys. Rev.,133:A224 (1964).
R. Abe,Prog. Theor. Phys. (Kyoto) 47:62, 1200 (1972).
K. G. Wilson and M. E. Fisher,Phys. Rev. Lett. 28:240 (1972).
K. G. Wilson and J. B. Kogut,Phys. Rep. 12C:75 (1974); M. E. Fisher,Rev. Mod. Phys. 46:597 (1974). S-K. Ma,Modern Theory of Critical Phenomena (Benjamin, Reading, Massachusetts, 1976).
P. R. Gerber and M. E. Fisher,Phys. Rev. B 10:4697 (1974).
E. Brezin, J. C. LeGuillou, and J. Zinn-Justin,Phys. Rev. D 15:1544 (1977).
K. G. Wilson (private communication, 1972).
T. D. Lee and C. N. Yang,Phys. Rev. 87:410 (1952).
E. H. Lieb and A. D. Sokal,Commun. Math. Phys. 80:153 (1981).
E. T. Copson,Theory of Functions of a Complex Variable (Oxford, London, 1948).
G. A. Baker, Jr.,Phys. Rev. Lett. 20:990 (1968).
J. D. Bessis, J. M. Drouffe, and P. Moussa,J. Phys. A 9:2105 (1976).
G. A. Baker, Jr.,Essentials of Fade Approximants (Academic, New York, 1975).
H. S. Wall,Analytic Theory of Continued Fractions (Van Nostrand, New York, 1948).
G. A. Baker, Jr.,Phys. Rev. B 15:1552 (1977).
G. S. Rushbrooke and H. I. Scoins,Proc. R. Soc. London A230:74 (1955).
T. L. Hill,Statistical Mechanics (McGraw-Hill, New York, 1956).
Y. Gefen, B. B. Mandelbrot, and A. Aharony,Phys. Rev. Lett. 45:855 (1980).
K. G. Wilson,Phys. Rev. Lett. 28:548 (1972).
E. Brezin, J. C. LeGuillou, and J. Zinn-Justin, inPhase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1976), Vol. 6, pp. 125–247.
B. O. Peirce,A Short Table of Integrals, 2nd ed. (Ginn, Boston, 1910).
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions, Natl. Bur. Stand., Appl. Math. Ser. No. 55 (US GPO, Washington, DC, 1964), Eq. (9.6.18).
W. Gröbner and N. Hofreiter,Integraltafeln, Part II, 4th ed. (Springer-Verlag, Vienna, 1966), Eq. (5.31.4b).
E. Montroll and G. H. Weiss,J. Math. Phys. 6:167 (1965).
E. F. Beckenbach and R. Bellman,Inequalities (Springer-Verlag, New York, 1965), Sec. 14, Chap. 1.
G. S. Joyce, inPhase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, London, 1972), Vol. 2, pp. 375–442.
G. 't Hooft and M. Veltman,Nucl. Phys. B 44:189 (1972).
V. Rivasseau and E. Speer,Commun. Math. Phys. 72:293 (1980).
B. Simon and R. B. Griffiths,Commun. Math. Phys. 33:145 (1973);Phys. Rev. Lett. 30:931 (1973).
G. A. Baker, Jr. and D. Kim,J. Phys. A 13:L103 (1980).
J. W. Essam and M. E. Fisher,J. Chem. Phys. 38:802 (1963).
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Work supported in part by the US DOE.
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Baker, G.A., Benofy, L.P. On the ferromagnetic Ising model in noninteger spatial dimension. J Stat Phys 29, 699–716 (1982). https://doi.org/10.1007/BF01011786
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DOI: https://doi.org/10.1007/BF01011786