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Prog. Theor. Phys. Vol. 44 No. 6 (1970) pp. 1477-1499

[ Full Text PDF : FREE ACCESS (1408K) ]

Dynamic Susceptibility of Classical Anharmonic Oscillator

— A Unified Oscillator Model for Order-Disorder and Displacive Ferroelectrics —

Yositaka Onodera

Department of Physics, Kyoto University, Kyoto

(Received August 6, 1970)

Abstract:

As a unified oscillator model for order-disorder and displacive ferroelectrics, we consider a system of interacting classical oscillators moving in the anharmonic potential V(x) = Ax4 + Bx2, where A is positive and B may be either positive or negative. The interaction of the oscillators is taken to be bilinear in their displacements and it is treated in the Weiss molecular-field approximation. For this model, it is shown that the exact expression can be obtained for the dynamic susceptibility above the Curie temperature. The theory is exact except for its being classical and use of the Weiss approximation; anharmonicity of the potential is perfectly taken into account. Detailed analysis is made for this system and temperature dependence of the dynamic response (including the occurrence of “soft” mode) is described on the basis of the results of numerical calculations for both B > 0 and B < 0 cases.


URL : http://ptp.ipap.jp/link?PTP/44/1477/
DOI : 10.1143/PTP.44.1477

[ Full Text PDF : FREE ACCESS (1408K) ] Citation:

References:

  1. V. G. Vaks, V. M. Galitskii and A. I. Larkin, Zh. Eksp. Teor. Fiz. 51 (1966), 1592.
  2. K. Aizu, J. Phys. Soc. Jpn. 21 (1966), 1240[JPSJ].
  3. M. E. Lines, Phys. Rev. 177 (1969), 797[APS].
  4. R. Kubo, J. Phys. Soc. Jpn. 12 (1957), 570[JPSJ].
  5. D. N. Zubarev, Uspekhi Fiz. Nauk SSSR 71 (1960), 71.
  6. See, for example, L. D. Landau and E. M. Lifshits, Kvantovaya Mekhanika (Fizmatgiz, Moskow, 1963), Appendix d, Confluent hypergeometric function.
  7. A number of useful formulae concerning the elliptic functions are compiled by P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists (Springer-Verlag, 1954).
  8. M. Suzuki, to be published in Physica.

Citing Article(s) :

  1. Journal of the Physical Society of Japan 58 (1989) pp. 3227-3235 :
    Two Kinds of Dipole Moments in Ferroelectric Phase Transitions in Terms of a Coupled Anharmonic-Oscillator Model
    Yositaka Onodera and Norimichi Kojyo
  2. Journal of the Physical Society of Japan 59 (1990) pp. 4488-4493 :
    Phase Transition of (NH4)2SO4-K2SO4 Mixed Crystal
    Katsuhiko Fujii, Hiroshi Mori and Takeo Matsubara
  3. Journal of the Physical Society of Japan 60 (1991) pp. 1247-1256 :
    Correlation between Transition Entropy and the Rhodes-Wohlfarth Ratio in Ferroelectric Materials
    Yositaka Onodera and Nobuyuki Sawashima
  4. Journal of the Physical Society of Japan 63 (1994) pp. 904-914 :
    Orientational Phase Transition and Dynamic Susceptibility of Hindered-Rotating Dipolar System –A Librator-Rotator Model–
    Yoshiki Nakajima and Shigeo Naya
  5. Journal of the Physical Society of Japan 63 (1994) pp. 3619-3628 :
    Phase Transition and Dynamic Susceptibility of the Anharmonic Oscillator System –An Effective Analysis of Double Morse Potential Based on the Unified Oscillator Model–
    Yoshiki Nakajima and Shigeo Naya
  6. Journal of the Physical Society of Japan 64 (1995) pp. 4646-4652 :
    Landau Free Energy in the Mean-Field Approximation for Coupled Classical Anharmonic Oscillators
    Sumiaki Wada and Yositaka Onodera
  7. Journal of the Physical Society of Japan 67 (1998) pp. 3137-3140 :
    Distortion of Local Order Parameter Caused by Impurities in Displacive Phase Transition*
    Kazuya Saito
  8. Journal of the Physical Society of Japan 72 (2003) pp. 727-729 :
    Instability of the Order–Disorder Ferroelectrics
    Katsuhiko Fujii, Yutaka Aikawa and Yojiro Shimazutsu
  9. Journal of the Physical Society of Japan 73 (2004) pp. 1216-1221 :
    Dynamical Response of Ferroelectrics in Terms of a Classical Anharmonic-Oscillator Model
    Yositaka Onodera
  10. Journal of the Physical Society of Japan 73 (2004) pp. 3466-3470 :
    Dynamical Susceptibility of Proton in a Two-Morse Potential
    Hiroyuki Mashiyama
  11. Journal of the Physical Society of Japan 77 (2008) 084709 (6 pages) :
    Order–Disorder and Displacive Transitions in a Quantum Ising Model
    Hiroyuki Mashiyama, Serges Eric Mkam Tchouobiap, and Masami Ashida
  12. Progress of Theoretical Physics Vol. 45 No. 3 (1971) pp. 986-988 :
    Free Energy and Specific Heat in Ferroelectric Phase Transition in Terms of a Single-Mode Anharmonic Oscillator Model
    Yositaka Onodera
  13. Progress of Theoretical Physics Vol. 48 No. 1 (1972) pp. 351-353 :
    A Note on Dynamic Susceptibility of Classical Non-Linear Oscillator
    Takeo Matsubara
  14. Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 699-712 :
    Dynamical Structure Factor of a Classical Anharmonic Oscillator
    Masao Iwamatsu and Yositaka Onodera
  15. Progress of Theoretical Physics Vol. 68 No. 2 (1982) pp. 374-387 :
    Freeze-In Transition of Anharmonic Oscillator System with Quenched Random Interactions
    Shinji Nambu and Shigeo Naya
  16. Progress of Theoretical Physics Vol. 78 No. 2 (1987) pp. 177-179 :
    Note on Temperature Dependence of Debye-Waller Factor in a Unified Model of Ferroelectrics
    Katsuhiko Fujii and Takeo Matsubara
  17. Progress of Theoretical Physics Vol. 78 No. 4 (1987) pp. 766-779 :
    The Birkhoff-Gustavson Normal Form of Double-Well Anharmonic Oscillators
    M. K. Ali and W. Robert Wood

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