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  • variational principle  (2)
  • Lifshitz point  (1)
  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 46 (1987), S. 971-982 
    ISSN: 1572-9613
    Schlagwort(e): Kac potential ; mean-field theory ; variational principle ; helicoidal phase ; crossover ; Lifshitz point
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider an Ising model with Kac potential γdK(γ¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limitγ→0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp 0≠0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2π/¦p 0¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 51 (1988), S. 519-536 
    ISSN: 1572-9613
    Schlagwort(e): Mean-field theory ; variational principle ; modulated phase ; ANNNI model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The mean-field theory of an Ising magnet with infinitely weak, infinitely long-range potentials of arbitrary sign is presented in terms of a variational principle for the magnetization. Previous studies of the theory have revealed paramagnetic, ferromagnetic, and modulated phases. For a particular choice of potential, which is an obvious continuous version of the between-plane ANNNI model interaction, exact solutions of the stationary condition implied by the variational principle are obtained. This leads us to formulate a trial magnetization to well describe the modulated phase in general. To illustrate the utility of the trial magnetization, both analytic and numerical calculations are performed, which determine the wavenumber in certain portions of the modulated phase for the above-mentioned potential.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
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