465 research outputs found
Violation of ensemble equivalence in the antiferromagnetic mean-field XY model
It is well known that long-range interactions pose serious problems for the
formulation of statistical mechanics. We show in this paper that ensemble
equivalence is violated in a simple mean-field model of N fully coupled
classical rotators with repulsive interaction (antiferromagnetic XY model).
While in the canonical ensemble the rotators are randomly dispersed over all
angles, in the microcanonical ensemble a bi-cluster of rotators separated by
angle , forms in the low energy limit. We attribute this behavior to the
extreme degeneracy of the ground state: only one harmonic mode is present,
together with N-1 zero modes. We obtain empirically an analytical formula for
the probability density function for the angle made by the rotator, which
compares extremely well with numerical data and should become exact in the zero
energy limit. At low energy, in the presence of the bi-cluster, an extensive
amount of energy is located in the single harmonic mode, with the result that
the energy temperature relation is modified. Although still linear, , it has the slope , instead of the canonical value
.Comment: 12 pages, Latex, 7 Figure
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.
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
Signature of magnetic monopole and Dirac string dynamics in spin ice
International audienceMagnetic monopoles have eluded experimental detection since their prediction nearly a century ago by Dirac. Recently it has been shown that classical analogues of these enigmatic particles occur as excitations out of the topological ground state of a model magnetic system, dipolar spin ice. These quasi-particle excitations do not require a modification of Maxwell's equations, but they do interact via Coulombs law and are of magnetic origin. In this paper we present an experimentally measurable signature of monopole dynamics and show that magnetic relaxation measurements in the spin ice material can be interpreted entirely in terms of the diffusive motion of monopoles in the grand canonical ensemble, constrained by a network of ``Dirac strings'' filling the quasi-particle vacuum. In a magnetic field the topology of the network prevents charge flow in the steady state, but there is a monopole density gradient near the surface of an open system
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
Direct calculation of the critical Casimir force in a binary fluid
We show that critical Casimir effects can be accessed through direct
simulation of a model binary fluid passing through the demixing transition. We
work in the semi grand canonical ensemble, in slab geometry, in which the
Casimir force appears as the excess of the generalized pressure,
. The excesses of the perpendicular pressure, , and of
, are individually of much larger amplitude. A critical pressure
anisotropy is observed between forces parallel and perpendicular to the
confinement direction, which collapses onto a universal scaling function
closely related to that of the critical Casimir force
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