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

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

Magnetocaloric Study of Spin Relaxation in `Frozen' Dipolar Spin Ice Dy2Ti2O7

The magnetocaloric effect of polycrystalline samples of pure and Y-doped dipolar spin ice Dy2Ti2O7 was investigated at temperatures from nominally 0.3 K to 6 K and in magnetic fields of up to 2 T. As well as being of intrinsic interest, it is proposed that the magnetocaloric effect may be used as an appropriate tool for the qualitative study of slow relaxation processes in the spin ice regime. In the high temperature regime the temperature change on adiabatic demagnetization was found to be consistent with previously published entropy versus temperature curves. At low temperatures (T < 0.4 K) cooling by adiabatic demagnetization was followed by an irreversible rise in temperature that persisted after the removal of the applied field. The relaxation time derived from this temperature rise was found to increase rapidly down to 0.3 K. The data near to 0.3 K indicated a transition into a metastable state with much slower relaxation, supporting recent neutron scattering results. In addition, magnetic dilution of 50 % concentration was found to significantly prolong the dynamical response in the milikelvin temperature range, in contrast with results reported for higher temperatures at which the spin correlations are suppressed. These observations are discussed in terms of defects and loop correlations in the spin ice state.Comment: 9 figures, submitted to Phys. Rev.

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

Dynamic behavior of magnetic avalanches in the spin-ice compound Dy2_2Ti2_2O7_7

Avalanches of the magnetization, that is to say an abrupt reversal of the magnetization at a given field, have been previously reported in the spin-ice compound Dy$_{2}$Ti$_{2}$O$_{7}$. This out-of-equilibrium process, induced by magneto-thermal heating, is quite usual in low temperature magnetization studies. A key point is to determine the physical origin of the avalanche process. In particular, in spin-ice compounds, the origin of the avalanches might be related to the monopole physics inherent to the system. We have performed a detailed study of the avalanche phenomena in three single crystals, with the field oriented along the [111] direction, perpendicular to [111] and along the [100] directions. We have measured the changing magnetization during the avalanches and conclude that avalanches in spin ice are quite slow compared to the avalanches reported in other systems such as molecular magnets. Our measurements show that the avalanches trigger after a delay of about 500 ms and that the reversal of the magnetization then occurs in a few hundreds of milliseconds. These features suggest an unusual propagation of the reversal, which might be due to the monopole motion. The avalanche fields seem to be reproducible in a given direction for different samples, but they strongly depend on the initial state of magnetization and on how the initial state was achieved.Comment: 11 pages, 14 figure

Overlap Distribution of the Three-Dimensional Ising Model

We study the Parisi overlap probability density P_L(q) for the three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations. At the critical point P_L(q) is peaked around q=0 in contrast with the double peaked magnetic probability density. We give particular attention to the tails of the overlap distribution at the critical point, which we control over up to 500 orders of magnitude by using the multi-overlap MC algorithm. Below the critical temperature interface tension estimates from the overlap probability density are given and their approach to the infinite volume limit appears to be smoother than for estimates from the magnetization.Comment: 7 pages, RevTex, 9 Postscript figure

Longitudinal changes in dietary patterns during adult life

Despite the growing interest in dietary patterns, there have been few longitudinal investigations. The objective of the present study was to extend an earlier method of dietary pattern assessment to longitudinal binary data and to assess changes in patterns over time and in relation to socio-demographic covariates. A prospective national cohort of 1265 participants completed a 5 d food diary at three time-points during their adult life (at age 36 years in 1982, 43 years in 1989 and 53 years in 1999). Factor analysis identified three dietary patterns for women (fruit, vegetables and dairy; ethnic foods and alcohol; meat, potatoes and sweet foods) and two patterns in men (ethnic foods and alcohol; mixed). Trends in dietary pattern scores were calculated using random effects models. Marked changes were found in scores for all patterns between 1989 and 1999, with only the meat, potatoes and sweet foods pattern in women recording a decline. In a multiple variable model that included the three time-points, socio-demographic variables and BMI time-dependent covariates, both non-manual social class and higher education level were also strongly associated with the consumption of more items from the ethnic foods and alcohol pattern and the mixed pattern for men (P&lt;0[middle dot]0001) and the fruit, vegetables and dairy pattern and the ethnic foods and alcohol pattern for women (P&lt;0[middle dot]01). In conclusion, longitudinal changes in dietary patterns and across socio-economic groups can assist with targeting public health initiatives by identifying stages during adult life when interventions to improve diet would be most beneficial to health.<br /

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]

Static Correlation and Dynamical Properties of Tb3+-moments in Tb2Ti2O7 -Neutron Scattering Study-

Static and dynamical properties of the magnetic moment system of pyrochlore compound Tb2Ti2O7 with strong magnetic frustration, have been investigated down to the temperature T=0.4 K by neutron scattering on a single crystal sample. The scattering vector (Q)-dependence of the magnetic scattering intensity becomes appreciable with decreasing T at around 30 K, indicating the development of the magnetic correlation. From the observed energy profiles, the elastic, quasi elastic and inelastic components have been separately obtained. The quasi elastic component corresponds to the diffusive motion of the magnetic moments within the lowest states, which are formed of the lowest energy levels of Tb3+ ions. Magnetic correlation pattern which can roughly reproduce the Q-dependence of the scattering intensities of the elastic and quasi elastic component is discussed based on the trial calculations for clusters of 7 moments belonging to two corner-sharing tetrahedra. A possible origin of the glassy state, which develops at around 1.5 K with decreasing T is discussed.Comment: 10 pages, 12 figures, to be published in J. Phys. Soc. Jpn. 71(2002)No.2 59

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, $\beta$, that characterize the evolution of the order parameter through the ordering transition. The distribution is found to be bimodal and bounded within a window $\sim 0.1 \le \beta \le 0.25$, 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