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.

Low-temperature muon spin rotation studies of the monopole charges and currents in Y doped Ho2Ti2O7

In the ground state of Ho2Ti2O7 spin ice, the disorder of the magnetic moments follows the same rules as the proton disorder in water ice. Excitations take the form of magnetic monopoles that interact via a magnetic Coulomb interaction. Muon spin rotation has been used to probe the low-temperature magnetic behaviour in single crystal Ho2−xYxTi2O7 (x = 0, 0.1, 1, 1.6 and 2). At very low temperatures, a linear field dependence for the relaxation rate of the muon precession λ(B), that in some previous experiments on Dy2Ti2O7 spin ice has been associated with monopole currents, is observed in samples with x = 0, and 0.1. A signal from the magnetic fields penetrating into the silver sample plate due to the magnetization of the crystals is observed for all the samples containing Ho allowing us to study the unusual magnetic dynamics of Y doped spin ice

Characterising anomalous transport in accretion disks from X-ray observations

Whilst direct observations of internal transport in accretion disks are not yet possible, measurement of the energy emitted from accreting astrophysical systems can provide useful information on the physical mechanisms at work. Here we examine the unbroken multi-year time variation of the total X-ray flux from three sources: Cygnus X-1 , the microquasar GRS 1915+105 , and for comparison the nonaccreting Crab nebula. To complement previous analyses, we demonstrate that the application of advanced statistical methods to these observational time-series reveals important contrasts in the nature and scaling properties of the transport processes operating within these sources. We find the Crab signal resembles Gaussian noise; the Cygnus X-1 signal is a leptokurtic random walk whose self-similar properties persist on timescales up to three years; and the GRS 1915+105 signal is similar to that from Cygnus X-1, but with self-similarity extending possibly to only a few days. This evidence of self-similarity provides a robust quantitative characterisation of anomalous transport occuring within the systems

Topological Sector Fluctuations and Curie Law Crossover in Spin Ice

At low temperatures, a spin ice enters a Coulomb phase - a state with algebraic correlations and topologically constrained spin configurations. In Ho2Ti2O7, we have observed experimentally that this process is accompanied by a non-standard temperature evolution of the wave vector dependent magnetic susceptibility, as measured by neutron scattering. Analytical and numerical approaches reveal signatures of a crossover between two Curie laws, one characterizing the high temperature paramagnetic regime, and the other the low temperature topologically constrained regime, which we call the spin liquid Curie law. The theory is shown to be in excellent agreement with neutron scattering experiments. On a more general footing, i) the existence of two Curie laws appears to be a general property of the emergent gauge field for a classical spin liquid, and ii) sheds light on the experimental difficulty of measuring a precise Curie-Weiss temperature in frustrated materials; iii) the mapping between gauge and spin degrees of freedom means that the susceptibility at finite wave vector can be used as a local probe of fluctuations among topological sectors.Comment: 10 pages, 5 figure

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

Ordered Phase of the Dipolar Spin Ice under [110]-Magnetic Fields

We find that the true ground state of the dipolar spin ice system under [110]-magnetic fields is the ``Q=X'' structure, which is consistent with both experiments and Monte Carlo simulations. We then perform a Monte Carlo simulation to confirm that there exists a first order phase transition under the [110]-field. In particular this result indicates the existence of the first order phase transition to the ``Q=X'' phase in the field above 0.35 T for Dy2Ti2O7. We also show the magnetic field-temperature phase diagram to summarize the ordered states of this system.Comment: 4 pages, 5 figures, in RevTex4, submitted to J. Phys. Soc. Jp

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

Long Range Order at Low Temperature in Dipolar Spin Ice

Recently it has been suggested that long range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$. We report here numerical results on the low temperature properties of the dipolar spin ice model, obtained via a new loop algorithm which greatly improves the dynamics at low temperature. We recover the previously reported missing entropy in this model, and find a first order transition to a long range ordered phase with zero total magnetization at very low temperature. We discuss the relevance of these results to ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$.Comment: New version of the manuscript. Now contains 3 POSTSCRIPT figures as opposed to 2 figures. Manuscript contains a more detailed discussion of the (i) nature of long-range ordered ground state, (ii) finite-size scaling results of the 1st order transition into the ground state. Order of authors has been changed. Resubmitted to Physical Review Letters Contact: [email protected]

Magnetic Monopole Dynamics in Spin Ice

One of the most remarkable examples of emergent quasi-particles, is that of the "fractionalization" of magnetic dipoles in the low energy configurations of materials known as "spin ice", into free and unconfined magnetic monopoles interacting via Coulomb's 1/r law [Castelnovo et. al., Nature, 451, 42-45 (2008)]. Recent experiments have shown that a Coulomb gas of magnetic charges really does exist at low temperature in these materials and this discovery provides a new perspective on otherwise largely inaccessible phenomenology. In this paper, after a review of the different spin ice models, we present detailed results describing the diffusive dynamics of monopole particles starting both from the dipolar spin ice model and directly from a Coulomb gas within the grand canonical ensemble. The diffusive quasi-particle dynamics of real spin ice materials within "quantum tunneling" regime is modeled with Metropolis dynamics, with the particles constrained to move along an underlying network of oriented paths, which are classical analogues of the Dirac strings connecting pairs of Dirac monopoles.Comment: 26 pages, 12 figure