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AIP conference proceedings

The anisotropic Heisenberg ferromagnet: Magnetization in a semi-infinite lattice

N. S. Branco, Anna Chame

Published Jan 1, 1996• 0 citations
Publisher

Abstract

Using a real space renormalization group procedure, we calculate both surface and bulk order parameters of the spin‐(1/2) anisotropic Heisenberg model in a semi‐infinite (d=3) lattice. We focus on the extraordinary transition, where the bulk disorders while the surface maintains its magnetization. We observe that the surface order parameter has a continuous first derivative at the bulk critical temperature, for all values of the anisotropy parameters ΔB and ΔS.

DOI
10.1063/1.51142

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Using a real space renormalization group procedure, we calculate both surface and bulk order parameters of the spin‐(1/2) anisotropic Heisenberg model in a semi‐infinite (d=3) lattice. We focus on the extraordinary transition, where the bulk disorders while the surface maintains its magnetization. We observe that the surface order parameter has a continuous first derivative at the bulk critical temperature, for all values of the anisotropy parameters ΔB and ΔS.
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).
Using a recently introduced renormalisation group method, the authors study the behaviour of the spontaneous surface and bulk magnetisations as functions of the temperature for an Ising ferromagnet in a semi-infinite cubic lattice for various J S /J B ratios (J S and J B respectively are the surface and bulk coupling constants). In particular, they study the extraordinary transition where the surface maintains its magnetisation as the bulk disorders: the authors find a discontinuity in the first derivative of the surface magnetisation at the bulk transition temperature. The criticality of the system (universality classes, critical exponents and amplitudes) is discussed as well.
We use a Migdal-Kadanoff-like renormalization group approach to study the critical behaviour of a semi-infinite simple cubic Ising ferromagnet whose (1, 0, 0) free surface contains anisotropic (in spin space) Heisenberg ferromagnetic interactions. The phase diagram presents three phases (namely the paramagnetic, the bulk ferromagnetic and the surface ferromagnetic ones) which join on a multicritical point The location of this point is calculated as a function of the anisotropy. The various universality classes of the problem are exhibited.
We consider two semi-infinite spin-1/2 Ising media (respectively characterized by the ferromagnetic coupling constants J1{J}_{1}J1​ and J2{J}_{2}J2​) separated by a spin-1/2 anisotropic Heisenberg interface (characterized by a ferromagnetic coupling constant JS{J}_{S}JS​ 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 J1{J}_{1}J1​=J2{J}_{2}J2​ case.