Prog. Theor. Phys. Vol. 45 No. 5 (1971) pp. 1407-1436

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A Dynamic Approach to Phase Transition Based on Moments

— Quasi-Collective Mode and the Range of Coherence —

Kazuhisa Tomita and Hiroyuki Tomita

Department of Physics, Faculty of Science, University of Kyoto, Kyoto

(Received November 16, 1970)

Abstract:

The inelastic magnetic scattering of neutron from a Heisenberg spin system is discussed with the use of the canonical correlation function. The second and fourth moments of the canonical correlation function are calculated in the paramagnetic range including the critical region of phase transition. Using these moments, and adopting a Gaussian torque assumption, the temperature and wavelength dependence of the width and the shape of the spectrum are derived. The results expalin various aspects of the recent experiments on RbMnF₃ qualitatively and semi-quantitatively. Among others the criterion is discussed for a quasi-collective mode to appear in the paramagnetic range with reference to Bennett's work.

URL : http://ptp.ipap.jp/link?PTP/45/1407/
DOI : 10.1143/PTP.45.1407

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In the coordinate space Kuramoto's formula, i.e. Eq. (50), means
<S₀ ·S_{R_c} >/ <S₀ ·S₀ >∼η( <1). (R_c=k_c^-1)
Lines introduced a similar concept coherence length L through a relation
<S₀·S_L >/ <S₀·S_Λ>= Φ(<1),
which is reduced to Kuramoto's definition when Λ is taken to be 0.

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