Deep radio observations of the radio halo of the bullet cluster 1E 0657-55.8

We present deep 1.1-3.1 GHz Australia Telescope Compact Array observations of the radio halo of the bullet cluster, 1E 0657-55.8. In comparison to existing images of this radio halo the detection in our images is at higher significance. The radio halo is as extended as the X-ray emission in the direction of cluster merger but is significantly less extended than the X-ray emission in the perpendicular direction. At low significance we detect a faint second peak in the radio halo close to the X-ray centroid of the smaller sub-cluster (the bullet) suggesting that, similarly to the X-ray emission, the radio halo may consist of two components. Finally, we find that the distinctive shape of the western edge of the radio halo traces out the X-ray detected bow shock. The radio halo morphology and the lack of strong point-to-point correlations between radio, X-ray and weak-lensing properties suggests that the radio halo is still being formed. The colocation of the X-ray shock with a distinctive radio brightness edge illustrates that the shock is influencing the structure of the radio halo. These observations support the theory that shocks and turbulence influence the formation and evolution of radio halo synchrotron emission.Comment: 15 pages, 16 figures, 3 tables. Accepted by MNRA

A very fast inference algorithm for finite-dimensional spin glasses: Belief Propagation on the dual lattice

Starting from a Cluster Variational Method, and inspired by the correctness of the paramagnetic Ansatz (at high temperatures in general, and at any temperature in the 2D Edwards-Anderson model) we propose a novel message passing algorithm --- the Dual algorithm --- to estimate the marginal probabilities of spin glasses on finite dimensional lattices. We show that in a wide range of temperatures our algorithm compares very well with Monte Carlo simulations, with the Double Loop algorithm and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover it is usually 100 times faster than other provably convergent methods, as the Double Loop algorithm.Comment: 23 pages, 12 figures. v2: improved introductio

Glauber Critical Dynamics: Exact Solution of the Kinetic Gaussian Model

In this paper, we have exactly solved Glauber critical dynamics of the Gaussian model on three dimensions. Of course, it is much easy to apply to low dimensional case. The key steps are that we generalize the spin change mechanism from Glauber's single-spin flipping to single-spin transition and give a normalized version of the transition probability . We have also investigated the dynamical critical exponent and found surprisingly that the dynamical critical exponent is highly universal which refer to that for one- two- and three-dimensions they have same value independent of spatial dimensionality in contrast to static (equilibrium) critical exponents.Comment: 9 page

Scattering phases for meson and baryon resonances on general moving-frame lattices

A proposal by L\"uscher enables one to compute the scattering phases of elastic two-body systems from the energy levels of the lattice Hamiltonian in a finite volume. In this work we generalize the formalism to S--, P-- and D--wave meson and baryon resonances, and general total momenta. Employing nonvanishing momenta has several advantages, among them making a wider range of energy levels accessible on a single lattice volume and shifting the level crossing to smaller values of $m_\pi L$.Comment: 41 pages, 3 figures. References added, minor edits to text. Version to be published in Phys. Rev.

Solvable Kinetic Gaussian Model in External Field

In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic lattice Gaussian spin system with Fourier's transformation method. We obtain exactly the local magnetization and the equal-time pair correlation function. The critical characteristics of the dynamical, the complex susceptibility, and the dynamical response are discussed. The results show that the time evolution of the dynamical quantities and the dynamical responses of the system strongly depend on the frequency and the wave vector of the external field.Comment: 11 page

Metastable states in the Blume-Emery-Griffiths spin glass model

We study the Blume-Emery-Griffiths spin glass model in presence of an attractive coupling between real replicas, and evaluate the effective potential as a function of the density overlap. We find that there is a region, above the first order transition of the model, where metastable states with a large density overlap exist. The line where these metastable states appear should correspond to a purely dynamical transition, with a breaking of ergodicity. Differently from what happens in p-spin glasses, in this model the dynamical transition would not be the precursor of a 1-step RSB transition, but (probably) of a full RSB transition.Comment: RevTeX, 4 pages, 2 fig

Characterizing and Improving Generalized Belief Propagation Algorithms on the 2D Edwards-Anderson Model

We study the performance of different message passing algorithms in the two dimensional Edwards Anderson model. We show that the standard Belief Propagation (BP) algorithm converges only at high temperature to a paramagnetic solution. Then, we test a Generalized Belief Propagation (GBP) algorithm, derived from a Cluster Variational Method (CVM) at the plaquette level. We compare its performance with BP and with other algorithms derived under the same approximation: Double Loop (DL) and a two-ways message passing algorithm (HAK). The plaquette-CVM approximation improves BP in at least three ways: the quality of the paramagnetic solution at high temperatures, a better estimate (lower) for the critical temperature, and the fact that the GBP message passing algorithm converges also to non paramagnetic solutions. The lack of convergence of the standard GBP message passing algorithm at low temperatures seems to be related to the implementation details and not to the appearance of long range order. In fact, we prove that a gauge invariance of the constrained CVM free energy can be exploited to derive a new message passing algorithm which converges at even lower temperatures. In all its region of convergence this new algorithm is faster than HAK and DL by some orders of magnitude.Comment: 19 pages, 13 figure

Replica Cluster Variational Method: the Replica Symmetric solution for the 2D random bond Ising model

We present and solve the Replica Symmetric equations in the context of the Replica Cluster Variational Method for the 2D random bond Ising model (including the 2D Edwards-Anderson spin glass model). First we solve a linearized version of these equations to obtain the phase diagrams of the model on the square and triangular lattices. In both cases the spin-glass transition temperatures and the tricritical point estimations improve largely over the Bethe predictions. Moreover, we show that this phase diagram is consistent with the behavior of inference algorithms on single instances of the problem. Finally, we present a method to consistently find approximate solutions to the equations in the glassy phase. The method is applied to the triangular lattice down to T=0, also in the presence of an external field.Comment: 22 pages, 11 figure