Abstract
A renormalization group method is used to construct approximants for the magnetization,m, and the static structure factor,\(\tilde C\)(q), for the simple cubic Ising model. Using the “best” values for the thermal critical index, the transition temperature, and the nearest-neighbor correlation function as input, we obtain recursion relations form and\(\tilde C\)(q) which lead to reasonable results over a wide range of temperatures and wave numbers.
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References
G. F. Mazenko and O. T. Valls, inReal Space Renormalization, J. M. J. van Leeuwen and T. N. Burkhardt, eds. (Springer, New York, 1982).
L. Onsager,Phys. Rev. 65:117 (1944).
G. F. Mazenko and O. T. Valls,Phys. Rev. B 24:1404 (1981).
G. F. Mazenko, J. Hirsch, M. Nolan, and O. T. Valls,Phys. Rev. Lett. 44:1083 (1980);Phys. Rev. B 23:1431 (1981).
M. E. Fisher and R. J. Burford,Phys. Rev. 156:583 (1967); H. B. Tarko and M. E. Fisher,Phys. Rev. B 11:121.7(1975).
J. C. LeGuillou and J. Zinn-Justin,Phys. Rev. Lett. 39:95 (1977).
B. Nickel,Physica 106A:48 (1981).
C. Domb, inPhase Transitions and Critical Phenomena, Vol. 3, C. Domb and M. S. Green, eds. (Academic Press, New York, 1972).
G. F. Mazenko and O. T. Valls,Phys. Rev. B 26:389 (1982).
J. Luscombe and G. F. Mazenko,Ann. Phys. 146:174 (1983).
S. K. Ma,Modern Theory of Critical Phenomena (Benjamin/Cummings, Reading, Massachusetts, 1976).
J. W. Essam and D. L. Hunter,J. Phys. C 1:392 (1968).
J. Als-Nielson,Phy. Rev. 185:664 (1969).
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Anderson, S.R., Mazenko, G.F. Construction of simple approximants for the structure factor and magnetization for the simple cubic Ising model. J Stat Phys 35, 1–18 (1984). https://doi.org/10.1007/BF01017361
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DOI: https://doi.org/10.1007/BF01017361