• Classical φ6-field theory in (1+1) dimensions. A model for structural phase transitions

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    • Keywords

       

      φ6-field theory; structural phase transitions; central peak; soft mode

    • Abstract

       

      The classical φ6-field theory in (1+1) dimensions, is considered as a model for the first order structural phase transitions. The equation of motion is solved exactly; and the presence of domain wall (kink) solutions at and below the transition point, in addition to the usual phonon-like oscillatory solutions, is demonstrated. The domain wall solutions are shown to be stable, and their mass and energies are calculated. Above the transition point there exists exotic unstable kink-like solutions which takes the particle from one hill top to the other of the potential. The partition function of the system is calculated exactly using the functional integral method together with the transfer matrix techniques which necessitates the determination of the eigenvalues of a Schrödinger-like equation. Thus the exact free energy is evaluated which in the low temperature limit has a phonon part and a contribution coming from the domain wall excitations. It was shown that this domain wall free energy differs from that calculated by the use of the domain wall phenomenology proposed by Krumhansl and Schrieffer. The exact solutions of the Schrödinger-like equation are also used to evaluate the displacement-displacement, intensity-intensity correlation functions and the probability distribution function. These results are compared with those obtained from the phenomenology as well as the φ4-field theory. A qualitative picture of the central peak observed in structural phase transitions is proposed.

    • Author Affiliations

       

      S N Behera1 Avinash Khare1 2

      1. Institute of Physics, A/105 Saheed Nagar, Bhubaneswar - 751 007, India
      2. Department of Theoretical Physics, University of Manchester, Manchester - M13, 9PL, England
    • Dates

       
  • Pramana – Journal of Physics | News

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