Generalized Ashkin-Teller model on the Bethe lattice Article

Rozenbaum, VM, Morozov, AN, Lin, SH. (2005). Generalized Ashkin-Teller model on the Bethe lattice . PHYSICAL REVIEW B, 71(19), 10.1103/PhysRevB.71.195411

cited authors

  • Rozenbaum, VM; Morozov, AN; Lin, SH

authors

abstract

  • A generalized Ashkin-Teller model is considered that includes both biquadratic and opposite in sign bilinear interactions between two Ising subsystems, σ and s, along horizontal and vertical bonds on the Bethe lattice with the coordination number 4 (interactions of this kind are typical of adsorbed lattice systems characterized by dipolelike intermolecular forces and a strong azimuthal angular dependence of the C4 -symmetrical adsorption potential). The exact solutions found in the framework of this model: (i) determine the second-order phase transitions between paraphase I with σ = s = σs =0 and two ordered phases, phase II with σ = s ≠0, σs ≠0, and phase III with σ ≠0 at σ = s =0 and (ii) specify the conditions for the conversion of second-order to first-order transitions. With regard to these solutions, the phase diagrams are constructed for K1, K2, K4, where Ki = Ji kB T, J1 is the interaction constant between σ-σ and s-s spin subsystems, J2 is the constant of bilinear fluctuation σ-s interactions, J4 is the constant of biquadratic σ-s interactions, kB is the Boltzmann constant, and T is the absolute temperature. First-order transitions are detected numerically by comparing the free energies of the phases concerned. It is shown that phase II is gradually replaced by phases I and III with rising J2 and vanishes at all if J2 = J1. © 2005 The American Physical Society.

publication date

  • December 13, 2005

published in

Digital Object Identifier (DOI)

volume

  • 71

issue

  • 19