Prog. Theor. Phys. Vol. 89 No. 5 (1993) pp. 985-993

[ Full Text PDF : FREE ACCESS (851K) ]

Anomalous Size Dependence of Relaxation Time in the Fuzzy Spin Model

— Mechanism of Slow Relaxation —

Department of Fundamental Sciences, Faculty of Integrated Human Studies, Kyoto University, Kyoto 606-01
^*Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-01

(Received January 5, 1993)

Abstract:

Slow relaxation phenomena are studied in the Fuzzy Spin Model which is a random Ising ferromagnetic model with random spin length. The model is found to have many metastable states, which cause an anomalous relaxation. Distribution of the relaxation time to the ferromagnetic equilibrium state is investigated by the Monte Carlo method after quenching rapidly the system (the two-dimensional square lattice) from infinite temperature to temperatures below the critical point. Up to a certain size, linear dimension L ≃20, the mean relaxation time increases exponentially with the size L as τ∝exp (aL) (a > 0), which is understood to be due to a relaxation based on overturns of strongly coupled domains. Above L ≃20, a different relaxation mechanism sets in, which shows a weaker size dependence. Mechanism of the size dependences of the relaxation is discussed in the viewpoint of distribution of the domains.

URL : http://ptp.ipap.jp/link?PTP/89/985/
DOI : 10.1143/PTP.89.985

References:

See, for example, A. T. Ogielski, Phys. Rev. B32 (1985), 7384[APS].
M. Randeria, J. P. Sethna and R. G. Palmer, Phys. Rev. Lett. 54 (1985), 1321[APS].
H. Takayama, private communication.
H. Takano and S. Miyashita, unpublished.
A. E. Jacobs and C. M. Coram, Phys. Rev. 36 (1987), 3844[APS].
T. Kawasaki, Prog. Theor. Phys. 80 (1988), 203[PTP]; 84 (1990), 213.
J.-S. Wang, W. Selke, Vl. S. Dotsenko and V. B. Andreichenko, Physica A164 (1990), 221.
S. Miyashita and H. Takano, Prog. Theor. Phys. 73 (1985), 73[PTP].
A. J. Bray, Phys. Rev. Lett. 60 (1988), 720[APS].
A. J. Bray and G. J. Rogers, Phys. Rev. B38 (1988), 9252[APS].
A. J. Bray and K. Humayum, J. of Phys. A24 (1991), L1185[IoP STACKS].
S. Puri, D. Chowdhury and N. Parekh, J. of Phys. A24 (1991), L1087[IoP STACKS].
D. Chowdhury, M. Grant and J. D. Gunton, Phys. Rev. B35 (1987), 6792[APS].
T. Nattermann, Y. Shapir and I. Vilfan, Phys. Rev. B42 (1990), 8577[APS].
H. Hayakawa, J. Phys. Soc. Jpn. 60 (1991), 2492[JPSJ].
D. A. Huse and C. L. Henley, Phys. Rev. Lett. 54 (1985), 2708[APS].
D. A. Huse, C. L. Henley and D. S. Fisher, Phys. Rev. Lett. 55 (1985), 2924[APS].
R. C. Tausworthe, Math. Comput. 19 (1965), 201.
S. Kirkpatrick and E. P. Stoll, J. Comp. Phys. 40 (1980), 517.
T. Kawasaki and S. Miyashita, J. Magn. Magn. Mater. 104-107 (1992), 1595[CrossRef].
S. Miyashita and T. Kawasaki, Relaxation Phenomena of the Fuzzy-Spin Model in AIP Conc. Proc. 256 (1992), p. 427.
T. Ohta, D. Jasnow and K. Kawasaki, Phys. Rev. Lett. 49 (1982), 1223[APS].
J. D. Gunton, M. San Miguel and P. S. Sahni, in Phase Transitions and Critical Phenomena, vol. 8, ed. C. Domb and J. L. Lebowitz (New York: Academic, 1983), p. 267.
H. Takano and S. Miyashita, in preparation.
H. Tomita and S. Miyashita, Phys. Rev. B46 (1992), 8886[APS].
N. Kawashima, in Computational Approaches in Condensed-Matter Physics, ed. S. Miyashita, M. Imada and H. Takayama (Springer-Verlag, 1992), p. 240.
N. Kawashima and M. Suzuki, J. of Phys. A52 (1992), 1055[IoP STACKS].

Citing Article(s) :

Journal of the Physical Society of Japan 78 (2009) 084002 (7 pages) :
Mechanism of Slow Relaxation due to Screening Effect in a Frustrated System

Shu Tanaka and Seiji Miyashita
Progress of Theoretical Physics Vol. 93 No. 1 (1995) pp. 47-54 :
Metastable Behavior in Relaxation Process of XY Fuzzy Spin Model

Tatuo Kawasaki and Seiji Miyashita