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

Electric Dipole Moments of Leptons in the Presence of Majorana Neutrinos

We calculate the two-loop diagrams that give a non-zero contribution to the electric dipole moment d_l of a charged lepton l due to possible Majorana masses of neutrinos. Using the example with one generation of the Standard Model leptons and two heavy right-handed neutrinos, we demonstrate that the non-vanishing result for d_l first appears in order O(m_l m_\nu^2 G_F^2), where m_\nu is the mass of the light neutrino and the see-saw type relation is imposed. This effect is beyond the reach of presently planned experiments.Comment: 13 page

Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model

We analyse the spin wave approximation for the 2D-XY model, directly in reciprocal space. In this limit the model is diagonal and the normal modes are statistically independent. Despite this simplicity non-trivial critical properties are observed and exploited. We confirm that the observed asymmetry for the probability density function for order parameter fluctuations comes from the divergence of the mode amplitudes across the Brillouin zone. We show that the asymmetry is a many body effect despite the importance played by the zone centre. The precise form of the function is dependent on the details of the Gibbs measure, giving weight to the idea that an effective Gibbs measure should exist in non-equilibrium systems, if a similar distribution is observed.Comment: 12 pages, 9 figure

Quasi-long-range ordering in a finite-size 2D Heisenberg model

We analyse the low-temperature behaviour of the Heisenberg model on a two-dimensional lattice of finite size. Presence of a residual magnetisation in a finite-size system enables us to use the spin wave approximation, which is known to give reliable results for the XY model at low temperatures T. For the system considered, we find that the spin-spin correlation function decays as 1/r^eta(T) for large separations r bringing about presence of a quasi-long-range ordering. We give analytic estimates for the exponent eta(T) in different regimes and support our findings by Monte Carlo simulations of the model on lattices of different sizes at different temperatures.Comment: 9 pages, 3 postscript figs, style files include

Width Distributions and the Upper Critical Dimension of KPZ Interfaces

Simulations of restricted solid-on-solid growth models are used to build the width-distributions of d=2-5 dimensional KPZ interfaces. We find that the universal scaling function associated with the steady-state width-distribution changes smoothly as d is increased, thus strongly suggesting that d=4 is not an upper critical dimension for the KPZ equation. The dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity.Comment: 4 pages, 4 postscript figures, RevTe

Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system

We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical over the whole of the low temperature phase. It is shown analytically and without recourse to the scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, independent of both system size and critical exponent $\eta$. An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high resolution molecular dynamics and Monte Carlo simulations. The calculation is extended to general dimension and an exponential tail is found in all dimensions less than four, despite the fact that critical fluctuations are limited to D=2. These results are discussed in the light of similar behaviour observed in models of interface growth and for dissipative systems driven into a non-equilibrium steady state.Comment: 32 pages, 13 figures, 1 table. Few changes. To appear in Phys. Rev.

Constraints on Low-Mass WIMP Interactions on 19F from PICASSO

Recent results from the PICASSO dark matter search experiment at SNOLAB are reported. These results were obtained using a subset of 10 detectors with a total target mass of 0.72 kg of 19F and an exposure of 114 kgd. The low backgrounds in PICASSO allow recoil energy thresholds as low as 1.7 keV to be obtained which results in an increased sensitivity to interactions from Weakly Interacting Massive Particles (WIMPs) with masses below 10 GeV/c^2. No dark matter signal was found. Best exclusion limits in the spin dependent sector were obtained for WIMP masses of 20 GeV/c^2 with a cross section on protons of sigma_p^SD = 0.032 pb (90% C.L.). In the spin independent sector close to the low mass region of 7 GeV/c2 favoured by CoGeNT and DAMA/LIBRA, cross sections larger than sigma_p^SI = 1.41x10^-4 pb (90% C.L.) are excluded.Comment: 23 pages, 7 figures, to be published in Phys. Lett.

The Tevatron at the Frontier of Dark Matter Direct Detection

Direct detection of dark matter (DM) requires an interaction of dark matter particles with nucleons. The same interaction can lead to dark matter pair production at a hadron collider, and with the addition of initial state radiation this may lead to mono-jet signals. Mono-jet searches at the Tevatron can thus place limits on DM direct detection rates. We study these bounds both in the case where there is a contact interaction between DM and the standard model and where there is a mediator kinematically accessible at the Tevatron. We find that in many cases the Tevatron provides the current best limit, particularly for light dark matter, below 5 GeV, and for spin dependent interactions. Non-standard dark matter candidates are also constrained. The introduction of a light mediator significantly weakens the collider bound. A direct detection discovery that is in apparent conflict with mono-jet limits will thus point to a new light state coupling the standard model to the dark sector. Mono-jet searches with more luminosity and including the spectrum shape in the analysis can improve the constraints on DM-nucleon scattering cross section.Comment: 20 pages, 8 figures, final version in JHE