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

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

Spin Dynamics at Very Low Temperature in Spin Ice Dy2_2Ti2_2O7_7

We have performed AC susceptibility and DC magnetic relaxation measurements on the spin ice system Dy$_2$Ti$_2$O$_7$ down to 0.08 K. The relaxation time of the magnetization has been estimated below 2 K down to 0.08 K. The spin dynamics of Dy$_2$Ti$_2$O$_7$ is well described by using two relaxation times ($\tau_{\rm S}$ (short time) and $\tau_{\rm L}$ (long time)). Both $\tau_{\rm S}$ and $\tau_{\rm L}$ increase on cooling. Assuming the Arrhenius law in the temperature range 0.5-1 K, we obtained an energy barrier of 9 K. Below 0.5 K, both $\tau_{\rm S}$ and $\tau_{\rm L}$ show a clear deviation from the thermal activated dynamics toward temperature independent relaxation, suggesting a quantum dynamics.Comment: 4 page

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

The complex universe: recent observations and theoretical challenges

The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical characterization of these structures shows that galaxy distribution is inhomogeneous in these samples, being characterized by large-amplitude fluctuations of large spatial extension. Over a large range of scales, both the average conditional density and its variance show a nontrivial scaling behavior: at small scales, r<20 Mpc/h, the average (conditional) density scales as 1/r. At larger scales, the density depends only weakly (logarithmically) on the system size and density fluctuations follow the Gumbel distribution of extreme value statistics. These complex behaviors are different from what is expected in a homogeneous distribution with Gaussian fluctuations. The observed density inhomogeneities pose a fundamental challenge to the standard picture of cosmology but it also represent an important opportunity which points to new directions with respect to many cosmological puzzles. Indeed, the fact that matter distribution is not uniform, in the limited range of scales sampled by observations, rises the question of understanding how inhomogeneities affect the large-scale dynamics of the universe. We discuss several attempts which try to model inhomogeneities in cosmology, considering their effects with respect to the role and abundance of dark energy and dark matter.Comment: 30 pages, 10 figure

Fluctuation and Dissipation in Liquid Crystal Electroconvection

In this experiment a steady state current is maintained through a liquid crystal thin film. When the applied voltage is increased through a threshold, a phase transition is observed into a convective state characterized by the chaotic motion of rolls. Above the threshold, an increase in power consumption is observed that is manifested by an increase in the mean conductivity. A sharp increase in the ratio of the power fluctuations to the mean power dissipated is observed above the transition. This ratio is compared to the predictions of the fluctuation theorem of Gallavotti and Cohen using an effective temperature associated with the rolls' chaotic motion.Comment: 4 pages, 3 figures, revtex forma

Cyprus' image—a sun and sea destination—as a detrimental factor to seasonal fluctuations. Exploration into motivational factors for holidaying in Cyprus

Cyprus is established as a summer destination. To aid the destination in developing its winter season as well, this research uses a qualitative inductive approach to explore the tourists’ current image of the island and their motivations of visiting it. The research indicates that the current image, which essentially portrays Cyprus as a sun-and-sea destination is thought to dissuade tourists from perceiving the island as a year-round destination. Nonetheless, increasing the pull factors of the destination through the development of unique special interest products can help in extending the tourism season as well as broaden its narrow image

Spin and orbital frustration in MnSc_2S_4 and FeSc_2S_4

Crystal structure, magnetic susceptibility, and specific heat were measured in the normal cubic spinel compounds MnSc_2S_4 and FeSc_2S_4. Down to the lowest temperatures, both compounds remain cubic and reveal strong magnetic frustration. Specifically the Fe compound is characterized by a Curie-Weiss temperature \Theta_{CW}= -45 K and does not show any indications of order down to 50 mK. In addition, the Jahn-Teller ion Fe^{2+} is orbitally frustrated. Hence, FeSc_2S_4 belongs to the rare class of spin-orbital liquids. MnSc_2S_4 is a spin liquid for temperatures T > T_N \approx 2 K.Comment: 4 pages, to be published in Physical Review Letter

Critical dynamics in the 2d classical XY-model: a spin dynamics study

Using spin-dynamics techniques we have performed large-scale computer simulations of the dynamic behavior of the classical three component XY-model (i.e. the anisotropic limit of an easy-plane Heisenberg ferromagnet), on square lattices of size up to 192^2, for several temperatures below, at, and above T_KT. The temporal evolution of spin configurations was determined numerically from coupled equations of motion for individual spins by a fourth order predictor-corrector method, with initial spin configurations generated by a hybrid Monte Carlo algorithm. The neutron scattering function S(q,omega) was calculated from the resultant space-time displaced spin-spin correlation function. Pronounced spin-wave peaks were found both in the in-plane and the out-of-plane scattering function over a wide range of temperatures. The in-plane scattering function S^xx also has a large number of clear but weak additional peaks, which we interpret to come from two-spin-wave scattering. In addition, we observed a small central peak in S^xx, even at temperatures well below the phase transition. We used dynamic finite size scaling theory to extract the dynamic critical exponent z. We find z=1.00(4) for all T <= T_KT, in excellent agreement with theoretical predictions, although the shape of S(q,omega) is not well described by current theory.Comment: 31 pages, LaTex, 13 figures (38 subfigures) included as eps-files, needs psfig, 260 K