1,859 research outputs found
Criterion for universality class independent critical fluctuations: example of the 2D Ising model
Order parameter fluctuations for the two dimensional Ising model in the
region of the critical temperature are presented. A locus of temperatures T*(L)
and of magnetic fields B*(L) are identified, for which the probability density
function is similar to that for the 2D-XY model in the spin wave
approximation.The characteristics of the fluctuations along these points are
largely independent of universality class. We show that the largest range of
fluctuations relative to the variance of the distribution occurs along these
loci of points, rather than at the critical temperature itself and we discuss
this observation in terms of intermittency. Our motivation is the
identification of a generic form for fluctuations in correlated systems in
accordance with recent experimental and numerical observations. We conclude
that a universality class dependent form for the fluctuations is a
particularity of critical phenomena related to the change in symmetry at a
phase transition.Comment: to appear in Phys. Rev.
Intermittency and non-Gaussian fluctuations of the global energy transfer in fully developed turbulence
We address the experimentally observed non-Gaussian fluctuations for the
energy injected into a closed turbulent flow at fixed Reynolds number. We
propose that the power fluctuations mirror the internal kinetic energy
fluctuations. Using a stochastic cascade model, we construct the excess kinetic
energy as the sum over the energy transfers at different levels of the cascade.
We find an asymmetric distribution that strongly resembles the experimental
data. The asymmetry is an explicit consequence of intermittency and the global
measure is dominated by small scale events correlated over the entire system.
Our calculation is consistent with the statistical analogy recently made
between a confined turbulent flow and a critical system of finite size.Comment: To appear in Physical Review Letter
Nature of finite-temperature transition in anisotropic pyrochlore Er2Ti2O7
We study the finite-temperature transition in a model XY antiferromagnet on a
pyrochlore lattice, which describes the pyrochlore material Er2Ti2O7. The
ordered magnetic structure selected by thermal fluctuations is six-fold
degenerate. Nevertheless, our classical Monte Carlo simulations show that the
critical behavior corresponds to the three-dimensional XY universality class.
We determine an additional critical exponent nu_6=0.75>nu characteristic of a
dangerously irrelevant scaling variable. Persistent thermal fluctuations in the
ordered phase are revealed in Monte Carlo simulations by the peculiar
coexistence of Bragg peaks and diffuse magnetic scattering, the feature also
observed in neutron diffraction experiments.Comment: 5+5 pages (including supplemental material
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
Crystal Shape-Dependent Magnetic Susceptibility and Curie Law Crossover in the Spin Ices Dy2Ti2O7 and Ho2Ti2O7
We present an experimental determination of the isothermal magnetic
susceptibility of the spin ice materials Dy2Ti2O7 and Ho2Ti2O7 in the
temperature range 1.8-300 K. The use of spherical crystals has allowed the
accurate correction for demagnetizing fields and allowed the true bulk
isothermal susceptibility X_T(T) to be estimated. This has been compared to a
theoretical expression based on a Husimi tree approximation to the spin ice
model. Agreement between experiment and theory is excellent at T > 10 K, but
systematic deviations occur below that temperature. Our results largely resolve
an apparent disagreement between neutron scattering and bulk measurements that
has been previously noted. They also show that the use of non-spherical
crystals in magnetization studies of spin ice may introduce very significant
systematic errors, although we note some interesting - and possibly new -
systematics concerning the demagnetizing factor in cuboidal samples. Finally,
our results show how experimental susceptibility measurements on spin ices may
be used to extract the characteristic energy scale of the system and the
corresponding chemical potential for emergent magnetic monopoles.Comment: 11 pages, 3 figures 1 table. Manuscript submitte
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