Geometry of rare regions behind Griffiths singularities in random quantum magnets

In many-body systems with quenched disorder, dynamical observables can be singular not only at the critical point, but in an extended region of the paramagnetic phase as well. These Griffiths singularities are due to rare regions, which are locally in the ordered phase and contribute to a large susceptibility. Here, we study the geometrical properties of rare regions in the transverse Ising model with dilution or with random couplings and transverse fields. In diluted models, the rare regions are percolation clusters, while in random models the ground state consists of a set of spin clusters, which are calculated by the strong disorder renormalization method. We consider the so called energy cluster, which has the smallest excitation energy and calculate its mass and linear extension in one-, two-and three-dimensions. Both average quantities are found to grow logarithmically with the linear size of the sample. Consequently, the energy clusters are not compact: for the diluted model they are isotropic and tree-like, while for the random model they are quasi-one-dimensional.

Anisotropic Metamaterials Filled Rectangular Metallic Waveguides Propagation Study and Analysis

In this paper, we propose a novel generalized S-matrix characterization approach. The goal is to keep track of all observed discontinuities as efficiently as possible. In terms of reflection value, the proposed control strategy is based on transmission coefficients and one-axis rectangular guides. We successfully manipulate metal rectangular waveguide filters with both geometrical and physical discontinuity. Lossless discontinuity is depicted as a periodic structure that contains Metamaterials. The modal development of transverse fields provides the basis for the generalized S-matrix approach. The approach works by breaking down electromagnetic fields for each of the guides that make up the discontinuity on an orthonormal basis. When the Galerkin method is used, the matrix of diffraction of the junction is obtained directly.

Temporal evolution of small-scale internetwork magnetic fields in the solar photosphere

Context. While the longitudinal field that dominates in photospheric network regions has been studied extensively, small-scale transverse fields have recently been found to be ubiquitous in the quiet internetwork photosphere and this merits further study. Furthermore, few observations have been able to capture how this field evolves. Aims. We aim to statistically characterize the magnetic vector in a quiet Sun internetwork region and observe the temporal evolution of specific small-scale magnetic features. Methods. We present two high spatio-temporal resolution observations that reveal the dynamics of two disk-centre internetwork regions taken by the new GREGOR Infrared Spectrograph Integral Field Unit with the highly magnetically sensitive photospheric Fe I line pair at 15648.52 Å and 15652.87 Å. We record the full Stokes vector and apply inversions with the Stokes inversions based on response functions code to retrieve the parameters characterizing the atmosphere. We consider two inversion schemes: scheme 1 (S1), where a magnetic atmosphere is embedded in a field free medium, and scheme 2 (S2), with two magnetic models and a fixed 30% stray light component. Results. The magnetic properties produced from S1 inversions returned a median magnetic field strength of 200 and 240 G for the two datasets, respectively. We consider the median transverse (horizontal) component, among pixels with Stokes Q or U, and the median unsigned longitudinal (vertical) component, among pixels with Stokes V, above a noise threshold. We determined the former to be 263 G and 267 G, and the latter to be 131 G and 145 G, for the two datasets, respectively. Finally, we present three regions of interest, tracking the dynamics of small-scale magnetic features. We apply S1 and S2 inversions to specific profiles of interest and find that the latter produces better approximations when there is evidence of mixed polarities. We find patches of linear polarization with magnetic flux density of the order of 130−150 G and find that linear polarization appears preferentially at granule-intergranular lane boundaries. The weak magnetic field appears to be organized in terms of complex ‘loop-like’ structures, with transverse fields often flanked by opposite polarity longitudinal fields.

Influence of the uniaxial stress $p_2$ and transverse fields $E_1$ and $E_3$ on the phase transitions and thermodynamic characteristics of GPI ferroelectric materials

A modified GPI model that accounts for the piezoelectric coupling between the ordered structural elements and the strains $\varepsilon_j$ has been used for studing of effects arising in GPI ferroelectrics under the action of the uniaxial stress $p_{2}$ and electric fields $E_1$ and $E_3$. The polarization vectors and components of static dielectric permittivity are calcucated in the two-particle cluster approximation for mechanically clamped crystal, and piezoelectric and thermal parameters are also determined. The influence of the simultaneous action of the stress $p_{2}$ and fields $E_1$ and $E_3$ on the phase transition and physical characteristics of GPI crystal has been studied.

Symmetry of Galactic Structure

It is hypothesized that due to mass-energy equivalence there exist transverse fields caused 7 by energy flows that are analogous to gravitomagnetic fields generated by mass flows. 8 Relativistically correct equations describing energy flow are derived by using the action integral of 9 a Lagrangian and assuming that the properties of energy, when described four-dimensionally with 10 time, are independent of the material system which supports them. The equations allow the 11 electromagnetic and gravitational energy flows to be compared revealing an underlying symmetry 12 of galactic structure.