Prog. Theor. Phys. Vol. 47 No. 1 (1972) pp. 62-68
Critical Exponent of the Ising Model in the High Density Limit
Department of Pure and Applied Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo
(Received July 30, 1971)
The system under consideration is the d-dimensional simple hypercubical Ising ferromagnet with nearest-neighbor interaction. A critical exponent γ for the susceptibility is discussed in the high density limit (d →∞), and formal expressions for γ in powers of 1/d are derived. It is shown that the expansion for γ is not determined uniquely, contrary to the case of Curie point. It is suggested that the deviation of γ from mean field result is proportional to exp(-Bd) in the high density limit, and B is estimated by an extrapolation method.
DOI : 10.1143/PTP.47.62
M. E. Fisher and D. S. Gaunt, Phys. Rev. 133 (1964), A224[APS].
- R. Abe, Prog. Theor. Phys. 33 (1965), 600[PTP].
G. Horwitz and H. B. Callen, Phys. Rev. 124 (1961), 1757[APS].
F. Englert, Phys. Rev. 129 (1963), 567[APS].
See also M. A. Moore, D. Jasnow and M. Wortis, Phys. Rev. Lett. 22 (1969), 940[APS].
- L. S. Ornstein and F. Zernike, Proc. Akad. Sci. (Amsterdam) 17 (1914), 793.
M. A. Moore, Phys. Rev. B 1 (1970), 2238[APS].
- S. Milo\usević and H. E. Stanley, J. de Phys. 32 (1971), C1-346.
- K. Kawasaki and T. Yamada, Prog. Theor. Phys. 39 (1968), 1[PTP].
Citing Article(s) :
Progress of Theoretical Physics Vol. 47 No. 4 (1972) pp. 1200-1203
Critical Exponent of the Ising Model in the High Density Limit. II
Progress of Theoretical Physics Vol. 56 No. 2 (1976) pp. 494-497
A Modified 1/d Expansion for Critical Temperature of Spherical Model on Hypercubic Lattice