655 research outputs found
Universal Magnetic Fluctuations with a Field Induced Length Scale
We calculate the probability density function for the order parameter
fluctuations in the low temperature phase of the 2D-XY model of magnetism near
the line of critical points. A finite correlation length, \xi, is introduced
with a small magnetic field, h, and an accurate expression for \xi(h) is
developed by treating non-linear contributions to the field energy using a
Hartree approximation. We find analytically a series of universal non-Gaussian
distributions with a finite size scaling form and present a Gumbel-like
function that gives the PDF to an excellent approximation. We propose the
Gumbel exponent, a(h), as an indirect measure of the length scale of
correlations in a wide range of complex systems.Comment: 7 pages, 4 figures, 1 table. To appear in Phys. Rev.
Competition Between Exchange and Anisotropy in a Pyrochlore Ferromagnet
The Ising-like spin ice model, with a macroscopically degenerate ground
state, has been shown to be approximated by several real materials. Here we
investigate a model related to spin ice, in which the Ising spins are replaced
by classical Heisenberg spins. These populate a cubic pyrochlore lattice and
are coupled to nearest neighbours by a ferromagnetic exchange term J and to the
local axes by a single-ion anisotropy term D. The near neighbour spin
ice model corresponds to the case D/J infinite. For finite D/J we find that the
macroscopic degeneracy of spin ice is broken and the ground state is
magnetically ordered into a four-sublattice structure. The transition to this
state is first-order for D/J > 5 and second-order for D/J < 5 with the two
regions separated by a tricritical point. We investigate the magnetic phase
diagram with an applied field along [1,0,0] and show that it can be considered
analogous to that of a ferroelectric.Comment: 7 pages, 4 figure
Statistics of extremal intensities for Gaussian interfaces
The extremal Fourier intensities are studied for stationary
Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We
calculate the probability distribution of the maximal intensity and find that,
generically, it does not coincide with the distribution of the integrated power
spectrum (i.e. roughness of the surface), nor does it obey any of the known
extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit
distribution is, however, recovered in three cases: (i) in the non-dispersive
(white noise) limit, (ii) for high dimensions, and (iii) when only
short-wavelength modes are kept. In the last two cases the limit distribution
emerges in novel scenarios.Comment: 15 pages, including 7 ps figure
Temperature Dependence of the Magnetic Penetration Depth in the Vortex State of the Pyrochlore Superconductor, Cd2Re2O7
We report transverse field and zero field muon spin rotation studies of the
superconducting rhenium oxide pyrochlore, Cd2Re2O7. Transverse field
measurements (H=0.007 T) show line broadening below Tc, which is characteristic
of a vortex state, demonstrating conclusively the type-II nature of this
superconductor. The penetration depth is seen to level off below about 400 mK
(T/Tc~0.4), with a rather large value of lambda (T=0)~7500A. The temperature
independent behavior below ~ 400 mK is consistent with a nodeless
superconducting energy gap. Zero-field measurements indicate no static magnetic
fields developing below the transition temperature.Comment: 4 pages, 4 figures, REVTEX 4, submitted to PR
Reply to Comment on " Universal Fluctuations in Correlated Systems"
Reply to the comment, cond-mat/0209398 by by N.W. Watkins, S.C. Chapman, and
G. RowlandsComment: To appear In Physical Review Letter
Low Temperature Spin Freezing in Dy2Ti2O7 Spin Ice
We report a study of the low temperature bulk magnetic properties of the spin
ice compound Dy2Ti2O7 with particular attention to the (T < 4 K) spin freezing
transition. While this transition is superficially similar to that in a spin
glass, there are important qualitative differences from spin glass behavior:
the freezing temperature increases slightly with applied magnetic field, and
the distribution of spin relaxation times remains extremely narrow down to the
lowest temperatures. Furthermore, the characteristic spin relaxation time
increases faster than exponentially down to the lowest temperatures studied.
These results indicate that spin-freezing in spin ice materials represents a
novel form of magnetic glassiness associated with the unusual nature of
geometrical frustration in these materials.Comment: 24 pages, 8 figure
Universal Fluctuations in Correlated Systems
The probability density function (PDF) of a global measure in a large class
of highly correlated systems has been suggested to be of the same functional
form. Here, we identify the analytical form of the PDF of one such measure, the
order parameter in the low temperature phase of the 2D-XY model. We demonstrate
that this function describes the fluctuations of global quantities in other
correlated, equilibrium and non-equilibrium systems. These include a coupled
rotor model, Ising and percolation models, models of forest fires, sand-piles,
avalanches and granular media in a self organized critical state. We discuss
the relationship with both Gaussian and extremal statistics.Comment: 4 pages, 2 figure
Universal Window for Two Dimensional Critical Exponents
Two dimensional condensed matter is realised in increasingly diverse forms
that are accessible to experiment and of potential technological value. The
properties of these systems are influenced by many length scales and reflect
both generic physics and chemical detail. To unify their physical description
is therefore a complex and important challenge. Here we investigate the
distribution of experimentally estimated critical exponents, , that
characterize the evolution of the order parameter through the ordering
transition. The distribution is found to be bimodal and bounded within a window
, facts that are only in partial agreement with
the established theory of critical phenomena. In particular, the bounded nature
of the distribution is impossible to reconcile with existing theory for one of
the major universality classes of two dimensional behaviour - the XY model with
four fold crystal field - which predicts a spectrum of non-universal exponents
bounded only from below. Through a combination of numerical and renormalization
group arguments we resolve the contradiction between theory and experiment and
demonstrate how the "universal window" for critical exponents observed in
experiment arises from a competition between marginal operators.Comment: 26 pages, 5 figures and 6 tables. Uses longtable packag
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