Intermittency and non-Gaussian fluctuations of the global energy transfer in fully developed turbulence

We address the experimentally observed non-Gaussian fluctuations for the energy injected into a closed turbulent flow at fixed Reynolds number. We propose that the power fluctuations mirror the internal kinetic energy fluctuations. Using a stochastic cascade model, we construct the excess kinetic energy as the sum over the energy transfers at different levels of the cascade. We find an asymmetric distribution that strongly resembles the experimental data. The asymmetry is an explicit consequence of intermittency and the global measure is dominated by small scale events correlated over the entire system. Our calculation is consistent with the statistical analogy recently made between a confined turbulent flow and a critical system of finite size.Comment: To appear in Physical Review Letter

Spin ice under pressure: symmetry enhancement and infinite order multicriticality

We study the low-temperature behaviour of spin ice when uniaxial pressure induces a tetragonal distortion. There is a phase transition between a Coulomb liquid and a fully magnetised phase. Unusually, it combines features of discontinuous and continuous transitions: the order parameter exhibits a jump, but this is accompanied by a divergent susceptibility and vanishing domain wall tension. All these aspects can be understood as a consequence of an emergent SU(2) symmetry at the critical point. We map out a possible experimental realisation

A Three Dimensional Kasteleyn Transition: Spin Ice in a [100] Field

We examine the statistical mechanics of spin-ice materials with a [100] magnetic field. We show that the approach to saturated magnetisation is, in the low-temperature limit, an example of a 3D Kasteleyn transition, which is topological in the sense that magnetisation is changed only by excitations that span the entire system. We study the transition analytically and using a Monte Carlo cluster algorithm, and compare our results with recent data from experiments on Dy2Ti2O7.Comment: 4 pages, 5 figure

Neel order, ring exchange and charge fluctuations in the half-filled Hubbard model

We investigate the ground state properties of the two dimensional half-filled one band Hubbard model in the strong (large-U) to intermediate coupling limit ({\it i.e.} away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order t(t/U)^3. We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as t/U is increased from the t/U -> 0 Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an S=1/2 antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of t/U, despite the fact that the moment of the spin Hamiltonien, which depends on transverse spin fluctuations only, in an increasing function of t/U. We also comment on quantitative aspects of the t/U and 1/S expansions.Comment: 9 pages - 3 figures - References and details to help the reader adde

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

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

Origin of the approximate universality of distributions in equilibrium correlated systems

We propose an interpretation of previous experimental and numerical experiments, showing that for a large class of systems, distributions of global quantities are similar to a distribution originally obtained for the magnetization in the 2D-XY model . This approach, developed for the Ising model, is based on previous numerical observations. We obtain an effective action using a perturbative method, which successfully describes the order parameter fluctuations near the phase transition. This leads to a direct link between the D-dimensional Ising model and the XY model in the same dimension, which appears to be a generic feature of many equilibrium critical systems and which is at the heart of the above observations.Comment: To appear in Europhysics Letter

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