Prog. Theor. Phys. Vol. 39 No. 2 (1968) pp. 349-364

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A Theory of the Second Order Phase Transitions in Spin Systems. III

— Critical Behavior of Correlation Functions in Ising Ferromagnets —

Masuo Suzuki

Department of Physics, Faculty of Science, University of Tokyo, Tokyo

(Received September 26, 1967)

Abstract:

Expressions for general correlation functions in Ising ferromagnets are derived in terms of the Lee-Yang theorem. By the use of these expressions, the asymptotic forms of correlation functions in the presence of magnetic field are analyzed, assuming those in the absence of the external field. In particular, the critical indices of spin-spin, energy-density-energy-density, energy-density-spin correlation functions are related with the critical indices of thermal susceptiblity χ_T⁰, specific heat, susceptibility χ_H⁰, and magnetization. These results agree in form with those predicted by the scaling law approach.

URL : http://ptp.ipap.jp/link?PTP/39/349/
DOI : 10.1143/PTP.39.349

References:

M. Suzuki, J. Phys. Soc. Jpn. 22 (1967), 757 [JPSJ](to be referred to as I).
M. Suzuki, Prog. Theor. Phys. 38 (1967), 289[PTP]; ibid. 38 (1967), 744 [PTP](to be referred to as L).
M. Suzuki, Prog. Theor. Phys. 38 (1967), 1225 [PTP](to be referred to as II).
T. D. Lee and C. N. Yang, Phys. Rev. 87 (1952), 410[APS].
L. P. Kadanoff, Physics 2 (1966), 263.
L. P. Kadanoff et al., Rev. Mod. Phys. 39 (1967), 395[APS].
R. Hecht, Phys. Rev. 158 (1967), 557[APS].
M. E. Fisher, Lectures in Theoretical Physics VII C, (1965), p. 1.
M. E. Fisher, preprint (review article).
J. W. Essam and M. E. Fisher, J. Chem. Phys. 38 (1963), 802[CrossRef].
R. Abe, Prog. Theor. Phys. 38 (1967), 72[PTP].
R. Abe, Prog. Theor. Phys. 38 (1967), 568[PTP].

Citing Article(s) :

Progress of Theoretical Physics Vol. 40 No. 4 (1968) pp. 706-733 :
Dynamics of Critical Fluctuations. III

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Progress of Theoretical Physics Vol. 40 No. 6 (1968) pp. 1246-1256 :
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Progress of Theoretical Physics Vol. 41 No. 6 (1969) pp. 1438-1449 :
On the Distribution of Zeros for the Heisenberg Model

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Progress of Theoretical Physics Vol. 42 No. 5 (1969) pp. 1076-1085 :
Singularity of Nonlinear Response near the Critical Field. I

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Progress of Theoretical Physics Vol. 43 No. 4 (1970) pp. 882-906 :
On the Singularity of Dynamical Response and Critical Slowing Down

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Progress of Theoretical Physics Vol. 44 No. 2 (1970) pp. 339-347 :
Some Remarks on Perturbation Theory and Phase Transition with an Application to Anisotropic Ising Model

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