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Fractals

DOMAIN WALLS IN THE TRANSVERSE FIELD ISING SPIN GLASSES

Mai Suan Li, Marek Cieplak

Published Sep 1, 1996• 0 citations
Publisher

Abstract

Interfaces in Ising spin glasses in the transverse field are studied by the local mean field method. The quantum fluctuations are found to make the length of domain walls shorter and smoother and to reduce the fractal dimensionality of the wall. The domain wall are almost as narrow as in the classical Ising case.
DOI
10.1142/s0218348x96000522

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Domain growth after a quench into the ordered phase is studied for the simple-cubic nearest-neighbor Gaussian Ising spin-glass model. A suitably defined time-averaged local overlap between two replicas is used to locate the domains and domain walls. The logarithmic domain growth rate dR(t)/d(logt), appears to increase with time t where R(t) is a measure of the linear size of the compact domains that are present. The effective fractal dimensionality of the domain walls is estimated. The bearing of the results on the many states versus two states controversy is briefly discussed.
We discuss several problems concerning domain walls in the spin-S Ising model at zero temeprature in a magnetic field, H/(2S), applied in the x direction. Some results are also given for the planar (y-z) model in a transverse field. We treat the quantum problem in one dimension by perturbation theory at small H and numerically over a large range of H. We obtain the spin-density profile by fixing the spins at opposite ends of the chain to have opposite signs of Sz{\mathit{S}}_{\mathit{z}}Sz​. One dimensional is special in that there the quantum width of the wall is proportional to the size L of the system. We also study the quantitative features of the ``particle'' band which extends up to energies of order H above the ground state. Except for the planar limit, this particle band is well separated from excitations having energy J/S involving creation of more walls. At large S this particle band develops energy gaps and the lowest subband has tunnel splittings of order H${2}^{1\mathrm{\ensuremath{-}}2\mathit{S}}$. This scale of of energy gives rise to anomalous scaling with respect to (a) finite size, (b) temperature, or (c) random potentials. The intrinsic width of the domain wall and the pinning energy are also defined and calculated in certain limiting cases. The general conclusion is that quantum effects prevent the wall from being sharp and in higher dimension would prevent sudden excursions in the configuration of the wall.
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We investigate analytically and numerically the dynamics of domain walls in a spin chain with ferromagnetic Ising interaction and subject to an external magnetic field perpendicular to the easy magnetization axis (transverse field Ising model). The analytical results obtained within the continuum approximation and numerical simulations performed for the discrete classical model are used to analyze the quantum properties of domain walls using the semiclassical approximation. We show that the domain wall spectrum shows a band structure consisting of 2S2S2S nonintersecting zones.