10 research outputs found
Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange
We study the one-dimensional quantum Heisenberg ferromagnet with exchange
couplings exhibiting long-range correlated disorder with power spectrum
proportional to , where is the wave-vector of the modulations
on the random coupling landscape. By using renormalization group, integration
of the equations of motion and exact diagonalization, we compute the spin-wave
localization length and the mean-square displacement of the wave-packet. We
find that, associated with the emergence of extended spin-waves in the
low-energy region for , the wave-packet mean-square displacement
changes from a long-time super-diffusive behavior for to a
long-time ballistic behavior for . At the vicinity of ,
the mobility edge separating the extended and localized phases is shown to
scale with the degree of correlation as .Comment: PRB to appea
Delocalization in harmonic chains with long-range correlated random masses
We study the nature of collective excitations in harmonic chains with masses
exhibiting long-range correlated disorder with power spectrum proportional to
, where is the wave-vector of the modulations on the random
masses landscape. Using a transfer matrix method and exact diagonalization, we
compute the localization length and participation ratio of eigenmodes within
the band of allowed energies. We find extended vibrational modes in the
low-energy region for . In order to study the time evolution of an
initially localized energy input, we calculate the second moment of
the energy spatial distribution. We show that , besides being dependent
of the specific initial excitation and exhibiting an anomalous diffusion for
weakly correlated disorder, assumes a ballistic spread in the regime
due to the presence of extended vibrational modes.Comment: 6 pages, 9 figure
Critical end point behaviour in a binary fluid mixture
We consider the liquid-gas phase boundary in a binary fluid mixture near its
critical end point. Using general scaling arguments we show that the diameter
of the liquid-gas coexistence curve exhibits singular behaviour as the critical
end point is approached. This prediction is tested by means of extensive
Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within
the grand canonical ensemble. The simulation results show clear evidence for
the proposed singularity, as well as confirming a previously predicted
singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev.
Lett. 65, 2402 (1990)]. The results suggest that the observed singularities,
particularly that in the coexistence diameter, should also be detectable
experimentally.Comment: 17 pages Revtex, 11 epsf figures. To appear in Phys. Rev.
Bosonic Excitations in Random Media
We consider classical normal modes and non-interacting bosonic excitations in
disordered systems. We emphasise generic aspects of such problems and parallels
with disordered, non-interacting systems of fermions, and discuss in particular
the relevance for bosonic excitations of symmetry classes known in the
fermionic context. We also stress important differences between bosonic and
fermionic problems. One of these follows from the fact that ground state
stability of a system requires all bosonic excitation energy levels to be
positive, while stability in systems of non-interacting fermions is ensured by
the exclusion principle, whatever the single-particle energies. As a
consequence, simple models of uncorrelated disorder are less useful for bosonic
systems than for fermionic ones, and it is generally important to study the
excitation spectrum in conjunction with the problem of constructing a
disorder-dependent ground state: we show how a mapping to an operator with
chiral symmetry provides a useful tool for doing this. A second difference
involves the distinction for bosonic systems between excitations which are
Goldstone modes and those which are not. In the case of Goldstone modes we
review established results illustrating the fact that disorder decouples from
excitations in the low frequency limit, above a critical dimension , which
in different circumstances takes the values and . For bosonic
excitations which are not Goldstone modes, we argue that an excitation density
varying with frequency as is a universal
feature in systems with ground states that depend on the disorder realisation.
We illustrate our conclusions with extensive analytical and some numerical
calculations for a variety of models in one dimension
Network models for localisation problems belonging to the chiral symmetry classes
We consider localisation problems belonging to the chiral symmetry classes,
in which sublattice symmetry is responsible for singular behaviour at a band
centre. We formulate models which have the relevant symmetries and which are
generalisations of the network model introduced previously in the context of
the integer quantum Hall plateau transition. We show that the generalisations
required can be re-expressed as corresponding to the introduction of absorption
and amplification into either the original network model, or the variants of it
that represent disordered superconductors. In addition, we demonstrate that by
imposing appropriate constraints on disorder, a lattice version of the Dirac
equation with a random vector potential can be obtained, as well as new types
of critical behaviour. These models represent a convenient starting point for
analytic discussions and computational studies, and we investigate in detail a
two-dimensional example without time-reversal invariance. It exhibits both
localised and critical phases, and band-centre singularities in the critical
phase approach more closely in small systems the expected asymptotic form than
in other known realisations of the symmetry class.Comment: 14 pages, 15 figures, Submitted to Physical Review
Magnetic Order and Disorder in the Frustrated Quantum Heisenberg Antiferromagnet in Two Dimensions
We have performed a numerical investigation of the ground state properties of the frustrated quantum Heisenberg antiferromagnet on the square lattice (“ model”), using exact diagonalization of finite clusters with 16, 20, 32, and 36 sites. Using a finite-size scaling analysis we obtain results for a number of physical properties: magnetic order parameters, ground state energy, and magnetic susceptibility (at ). In order to assess the reliability of our calculations, we also investigate regions of parameter space with well-established magnetic order, in particular the non-frustrated case . We find that in many cases, in particular for the intermediate region , the 16 site cluster shows anomalous finite size effects. Omitting this cluster from the analysis, our principal result is that there is Néel type order for and collinear magnetic order (wavevector Q
) for . An error analysis indicates uncertainties of order in the location of these critical values of . There thus is a region in parameter space without any form of magnetic order. For the unfrustrated case the results for order parameter, ground state energy, and susceptibility agree with series expansions and quantum Monte Carlo calculations to within a percent or better. Including the 16 site cluster, or analyzing the independently calculated magnetic susceptibility we also find a nonmagnetic region, but with modified values for the range of existence of the nonmagnetic region. From the leading finite-size corrections we also obtain results for the spin-wave velocity and the spin stiffness. The spin-wave velocity remains finite at the magnetic-nonmagnetic transition, as expected from the nonlinear sigma model analogy
Extended acoustic waves in a one-dimensional aperiodic system
We numerically study the propagation of acoustic waves in a one-dimensional system with an aperiodic pseudo-random elasticity distribution. The elasticity distribution was generated
by using a sinusoidal function whose phase
varies as a power-law, , where n labels the positions along the
media. By considering a discrete one-dimensional
version of the wave equation and a matrix recursive reformulation we compute the localization length within the band of allowed frequencies. In addition, we apply a second-order finite-difference
method for both the time and spatial variables and study the nature of the waves that propagate
in the chain. Our numerical data indicates the presence of extended acoustic waves with non-zero frequency for sufficient degree of aperiodicity