1,085 research outputs found
Generalised Longitudinal Susceptibility for Magnetic Monopoles in Spin Ice
The generalised longitudinal susceptibility affords a
sensitive measure of the spatial and temporal correlations of magnetic
monopoles in spin ice. Starting with the monopole model, a mean field
expression for is derived as well as expressions for
the mean square longitudinal field and induction at a point. Monopole motion is
shown to be strongly correlated, and both spatial and temporal correlations are
controlled by the dimensionless monopole density which defines the ratio of
the magnetization relaxation rate and the monopole hop rate. Thermal effects
and spin lattice relaxation are also considered. The derived equations are
applicable in the temperature range where the Wien effect for magnetic
monopoles is negligible. They are discussed in the context of existing theories
of spin ice and the following experimental techniques: dc and ac-magnetization,
neutron scattering, neutron spin echo, and longitudinal and transverse field
SR. The monopole theory is found to unify diverse experimental results,
but several discrepancies between theory and experiment are identified. One of
these, concerning the neutron scattering line shape, is explained by means of a
phenomenological modification to the theory.Comment: 29 pages, 4 figures; to be published in Phil. Trans A, special issue
for Royal Society Theo Murphy Meeting on Magnetic Monopoles in Spin Ice (Nov.
2011, UK). Second version, significantly revised after helpful referee
comments. Many typos correcte
Dynamic susceptibility and dynamic correlations in spin ice
Here we calculate the dynamic susceptibility and dynamic correlation function
in spin ice using the model of emergent magnetic monopoles. Calculations are
based on a method originally suggested for the description of dynamic processes
in water ice (non-equilibrium thermodynamics approach). We show that for zero
temperature the dynamic correlation function reproduces the transverse dipole
correlations (static correlation function) characteristic of spin ice in its
ground state. At non-zero temperatures the dynamic correlation function
includes an additional longitudinal component which decreases as the
temperature decreases. Both terms (transverse and longitudinal) exhibit
identical Debye-like dependences on frequency but with different relaxation
times: the magnetic Coulomb interaction of monopoles reduces the longitudinal
relaxation time with respect to the transverse one. We calculate the dielectric
function for the magnetic monopole gas and discuss how the non-equilibrium
thermodynamics approach exposes corrections to the Debye-Huckel theory of
magnetic monopoles and the concept of "entropic charge".Comment: 5 pages, 2 figure
Analytic form of a two-dimensional critical distribution
This paper explores the possibility of establishing an analytic form of the distribution of the order parameter fluctuations in a two-dimensional critical spin-wave model, or width fluctuations of a two-dimensional Edwards-Wilkinson interface. It is shown that the characteristic function of the distribution can be expressed exactly as a gamma function quotient, while a Charlier series, using the convolution of two Gumbel distributions as the kernel, converges to the exact result over a restricted domain. These results can also be extended to calculate the temperature dependence of the distribution and give an insight into the origin of Gumbel-like distributions in steady-state and equilibrium quantities that are not extreme values
An electric-field representation of the harmonic XY model
The two-dimensional harmonic XY (HXY) model is a spin model in which the
classical spins interact via a piecewise parabolic potential. We argue that the
HXY model should be regarded as the canonical classical lattice spin model of
phase fluctuations in two-dimensional condensates, as it is the simplest model
that guarantees the modular symmetry of the experimental systems. Here we
formulate a lattice electric-field representation of the HXY model and contrast
this with an analogous representation of the Villain model and the
two-dimensional Coulomb gas with a purely rotational auxiliary field. We find
that the HXY model is a spin-model analogue of a lattice electric-field model
of the Coulomb gas with an auxiliary field, but with a temperature-dependent
vacuum (electric) permittivity that encodes the coupling of the spin vortices
to their background spin-wave medium. The spin vortices map to the Coulomb
charges, while the spin-wave fluctuations correspond to auxiliary-field
fluctuations. The coupling explains the striking differences in the
high-temperature asymptotes of the specific heats of the HXY model and the
Coulomb gas with an auxiliary field. Our results elucidate the propagation of
effective long-range interactions throughout the HXY model (whose interactions
are purely local) by the lattice electric fields. They also imply that global
spin-twist excitations (topological-sector fluctuations) generated by local
spin dynamics are ergodically excluded in the low-temperature phase. We discuss
the relevance of these results to condensate physics.Comment: 13 pages, 10 figure
Topological-sector fluctuations and ergodicity breaking at the Berezinskii-Kosterlitz-Thouless transition
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the
unbinding of topological defects in many two-dimensional systems. In the
two-dimensional Coulomb gas, it corresponds to an insulator-conductor
transition driven by charge deconfinement. We investigate the global
topological properties of this transition, both analytically and by numerical
simulation, using a lattice-field description of the two-dimensional Coulomb
gas on a torus. The BKT transition is shown to be an ergodicity breaking
between the topological sectors of the electric field, which implies a
definition of topological order in terms of broken ergodicity. The breakdown of
local topological order at the BKT transition leads to the excitation of global
topological defects in the electric field, corresponding to different
topological sectors. The quantized nature of these classical excitations, and
their strict suppression by ergodicity breaking in the low-temperature phase,
afford striking global signatures of topological-sector fluctuations at the BKT
transition. We discuss how these signatures could be detected in experiments
on, for example, magnetic films and cold-atom systems.Comment: 11 pages, 6 figure
Comment on "Universal Fluctuations in Correlated Systems"
This is a Comment on "Universal Fluctuations in Correlated Systems".Comment: to appear in Phys. Rev. Let
Universal Fluctuations of the Danube Water Level: a Link with Turbulence, Criticality and Company Growth
A global quantity, regardless of its precise nature, will often fluctuate
according to a Gaussian limit distribution. However, in highly correlated
systems, other limit distributions are possible. We have previously calculated
one such distribution and have argued that this function should apply
specifically, and in many instances, to global quantities that define a steady
state. Here we demonstrate, for the first time, the relevance of this
prediction to natural phenomena. The river level fluctuations of the Danube are
observed to obey our prediction, which immediately establishes a generic
statistical connection between turbulence, criticality and company growth
statistics.Comment: 5 pages, 1 figur
Dilution effects in HoYSnO: from the Spin Ice to the single-ion magnet
A study of the modifications of the magnetic properties of
HoYSnO upon varying the concentration of diamagnetic
Y ions is presented. Magnetization and specific heat measurements show
that the Spin Ice ground-state is only weakly affected by doping for , even if non-negligible changes in the crystal field at Ho occur.
In this low doping range SR relaxation measurements evidence a
modification in the low-temperature dynamics with respect to the one observed
in the pure Spin Ice. For , or at high temperature, the dynamics
involve fluctuations among Ho crystal field levels which give rise to a
characteristic peak in Sn nuclear spin-lattice relaxation rate. In this
doping limit also the changes in Ho magnetic moment suggest a variation
of the crystal field parameters.Comment: 4 pages, 5 figures, proceedings of HFM2008 Conferenc
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