Europhysics Letters (EPL)

Influence of the Interaction Anisotropy on the Appearence of Surface Magnetism

Ananias M. Mariz, U.M.S. Costa, Constantino Tsallis

Published Jan 1, 1987• 22 citations

Abstract

Within a simple real space renormalization group scheme, we study the phase diagram of the d = 3 semi-infinite anisotropic Heisenberg ferromagnet with surface (bulk) coupling constant J s ( J B ) and anisotropy η s (η B ). We exhibit, in particular, the interesting effects of η s and η B on the (multicritical) ratio J s / J B above which surface order becomes observable even if bulk order is absent. Enhancement occurs for an Ising-like free surface (η s ≃ 1) on top of an isotropic-Heisenberg-like bulk (η B ≃ 0).

DOI: 10.1209/0295-5075/3/1/005

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Europhysics Letters (EPL)

Influence of the Interaction Anisotropy on the Appearence of Surface Magnetism

Ananias M. Mariz, U.M.S. Costa, Constantino Tsallis

Published Jan 1, 1987• 22 citations

Publisher

Abstract

DOI: 10.1209/0295-5075/3/1/005

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Roberto J. V. dos Santos, Enaldo F. Sarmento, Constantino Tsallis +1 more

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Hans Werner Diehl, Erich Eisenriegler

The critical behavior of a semi-infinite $n$ -vector model with anisotropic ferromagnetic pair interactions on the surface and isotropic interactions everywhere else is studied with the use of renormalization-group methods for dimension $d=4\ensuremath{-}\ensuremath{\epsilon}$. The effects of surface anisotropies are analyzed near the isotropic ordinary transition (where they produce corrections to scaling), near the isotropic special transition (where they are relevant perturbations), and near a new class of "anisotropic special" transitions. The latter occur if the surface exchange constants associated with ${m}_{e}$ (easy-magnetization) components take a critical value above which ${m}_{e}$ -component surface order is possible while the interaction constants of the remaining ${m}_{h}=n\ensuremath{-}{m}_{e}$ (hard-magnetization) components are weaker. Of particular interest is the anisotropic special transition with an easy axis ( ${m}_{e}=1$ ) because it occurs also in three dimensions, in contrast to the isotropic special one. The associated critical, crossover, and correction-to-scaling exponents are given to second order in $\ensuremath{\epsilon}$.The critical behavior of a semi-infinite $n$-vector model with anisotropic ferromagnetic pair interactions on the surface and isotropic interactions everywhere else is studied with the use of renormalization-group methods for dimension $d=4\ensuremath{-}\ensuremath{\epsilon}$. The effects of surface anisotropies are analyzed near the isotropic ordinary transition (where they produce corrections to scaling), near the isotropic special transition (where they are relevant perturbations), and near a new class of "anisotropic special" transitions. The latter occur if the surface exchange constants associated with ${m}_{e}$ (easy-magnetization) components take a critical value above which ${m}_{e}$-component surface order is possible while the interaction constants of the remaining ${m}_{h}=n\ensuremath{-}{m}_{e}$ (hard-magnetization) components are weaker. Of particular interest is the anisotropic special transition with an easy axis (${m}_{e}=1$) because it occurs also in three dimensions, in contrast to the isotropic special one. The associated critical, crossover, and correction-to-scaling exponents are given to second order in $\ensuremath{\epsilon}$.

Physical review. B, Condensed matterJul 1, 198440 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.

The critical behavior of a semi-infinite

n

-vector model with anisotropic ferromagnetic pair interactions on the surface and isotropic interactions everywhere else is studied with the use of renormalization-group methods for dimension $d=4\ensuremath{-}\ensuremath{\epsilon}$. The effects of surface anisotropies are analyzed near the isotropic ordinary transition (where they produce corrections to scaling), near the isotropic special transition (where they are relevant perturbations), and near a new class of "anisotropic special" transitions. The latter occur if the surface exchange constants associated with

{m}_{e}

(easy-magnetization) components take a critical value above which

{m}_{e}

-component surface order is possible while the interaction constants of the remaining ${m}_{h}=n\ensuremath{-}{m}_{e}$ (hard-magnetization) components are weaker. Of particular interest is the anisotropic special transition with an easy axis (

{m}_{e}=1

) because it occurs also in three dimensions, in contrast to the isotropic special one. The associated critical, crossover, and correction-to-scaling exponents are given to second order in $\ensuremath{\epsilon}$.