Physical review. B, Condensed matter

Critical surface coupling in anisotropic Heisenberg ferromagnets

Joaquim Nestor Braga de Moraes, W. Figueiredo

Published Dec 1, 1991• 7 citations

Abstract

We consider an anisotropic Heisenberg model on a semi-infinite cubic lattice within the Green-function formalism. We analyze various possible configurations for the surface and bulk anisotropy parameters. We determine a complete phase diagram for the multicritical points and our results are in agreement with real-space renormalization-group calculations.

DOI: 10.1103/physrevb.44.11784

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Physical review. B, Condensed matter

Critical surface coupling in anisotropic Heisenberg ferromagnets

Joaquim Nestor Braga de Moraes, W. Figueiredo

Published Dec 1, 1991• 7 citations

Publisher

Abstract

DOI: 10.1103/physrevb.44.11784

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physica status solidi (b)May 1, 20013 citations

We consider two semi-infinite spin-1/2 Ising media (respectively characterized by the ferromagnetic coupling constants

{J}_{1}

and

{J}_{2}

) separated by a spin-1/2 anisotropic Heisenberg interface (characterized by a ferromagnetic coupling constant

{J}_{S}

and by an anisotropy \ensuremath{\eta}\ensuremath{\in}[0,1] in spin space; \ensuremath{\eta}=1 and \ensuremath{\eta}=0, respectively, correspond to the Ising and isotropic Heisenberg limits). Within a real-space renormalization-group framework, we discuss the full phase diagram; this diagram exhibits, besides the paramagnetic phase, three physically different ordered phases, namely the double-bulk, single-bulk, and surface ferromagnetic ones. We also analyze the various universality classes appearing in this problem, and determine, in particular, the existence of a new high-order multicritical point associated with the

{J}_{1}

{J}_{2}

case.

Using a renormalization-group transformation in position space based on the Migdal-Kadanoff recursion relations, we investigate the three-dimensional semi-infinite cubic spin-

\frac{3}{2}

Blume-Emery-Griffiths model with single-site uniaxial anisotropy and nearest-neighbor pair interactions, both bilinear and biquadratic. The fixed-point topologies and corresponding phase diagrams predicted for this model are presented. Attention is focused on the renormalization-group description of the surface critical behaviors, in comparison with the mean-field approximation results. Three main classes of system phase diagrams are determined, featuring a rich variety of phase transitions associated with the surface with type being according to the values of bulk and surface interaction parameters. Surface critical, tricritical, bicritical, and multicritical points are also found.