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Prog. Theor. Phys. Vol. 39 No. 1 (1968) pp. 1-25

Time-Dependent Ising Model with Long Range Interaction

Kyozi Kawasaki and Tomoji Yamada

Department of Physics, Faculty of Science, Kyushu University, Fukuoka

(Received July 20, 1967)

Abstract:

A systematic method is developed for studying the time-dependent Ising model proposed by Glauber and extended by others. The graphical technique developed for the equilibrium statistical mechanics has been found to be useful in this nonequilibrium problem as well with some modifications. A hierarchy of equations linking various spin cluster functions is obtained. If we choose as the expansion parameter the reciprocal range of the spin interaction which is taken to be of Kac's type, the hierarchy is terminated, and closed sets of nonlinear kinetic equations satisfied by spin cluster functions follow. The dynamical susceptibility is studied using the hierachy, and the polydispersive nature of the spin relaxation is found to be closely connected to the deviation of the spin pair correlation from the Ornstein-Zernike form via multi-spin cluster functions. A sum rule on the distribution of relaxation times is found, which provides a precise expression for the critical slowing-down at the Curie point. The closed set of kinetic equations involving at most three spin cluster functions is used to evaluate explicitly the approximate dynamical susceptibility above the Curie point, and the characteristic time-scale of the polydispersive relaxation is found to increase indefinitely near the Curie point.

URL : http://ptp.ipap.jp/link?PTP/39/1/
DOI : 10.1143/PTP.39.1

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 39 No. 4 (1968) pp. 947-956 :

   Dynamics of the Ising Model near the Transition Point

   Ryuzo Abe

2. Progress of Theoretical Physics Vol. 39 No. 5 (1968) pp. 1133-1152 :

   Dynamics of Critical Fluctuations. I

   Kyozi Kawasaki

3. Progress of Theoretical Physics Vol. 40 No. 4 (1968) pp. 706-733 :

   Dynamics of Critical Fluctuations. III

   Kyozi Kawasaki

4. Progress of Theoretical Physics Vol. 43 No. 4 (1970) pp. 882-906 :

   On the Singularity of Dynamical Response and Critical Slowing Down

   Masuo Suzuki

5. Progress of Theoretical Physics Vol. 47 No. 1 (1972) pp. 62-68 :

   Critical Exponent of the Ising Model in the High Density Limit

   Ryuzo Abe

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