Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions

We consider disordered ladders of the transverse-field Ising model and study their critical properties and entanglement entropy for varying width, $w \le 20$, by numerical application of the strong disorder renormalization group method. We demonstrate that the critical properties of the ladders for any finite $w$ are controlled by the infinite disorder fixed point of the random chain and the correction to scaling exponents contain information about the two-dimensional model. We calculate sample dependent pseudo-critical points and study the shift of the mean values as well as scaling of the width of the distributions and show that both are characterized by the same exponent, $\nu(2d)$. We also study scaling of the critical magnetization, investigate critical dynamical scaling as well as the behavior of the critical entanglement entropy. Analyzing the $w$-dependence of the results we have obtained accurate estimates for the critical exponents of the two-dimensional model: $\nu(2d)=1.25(3)$, $x(2d)=0.996(10)$ and $\psi(2d)=0.51(2)$.Comment: 10 pages, 9 figure

Corner contribution to percolation cluster numbers in three dimensions

In three-dimensional critical percolation we study numerically the number of clusters, $N_{\Gamma}$, which intersect a given subset of bonds, $\Gamma$. If $\Gamma$ represents the interface between a subsystem and the environment, then $N_{\Gamma}$ is related to the entanglement entropy of the critical diluted quantum Ising model. Due to corners in $\Gamma$ there are singular corrections to $N_{\Gamma}$, which scale as $b_{\Gamma} \ln L_{\Gamma}$, $L_{\Gamma}$ being the linear size of $\Gamma$ and the prefactor, $b_{\Gamma}$, is found to be universal. This result indicates that logarithmic finite-size corrections exist in the free-energy of three-dimensional critical systems.Comment: 6 pages, 7 figures. arXiv admin note: text overlap with arXiv:1210.467

Boundary critical phenomena of the random transverse Ising model in D>=2 dimensions

Using the strong disorder renormalization group method we study numerically the critical behavior of the random transverse Ising model at a free surface, at a corner and at an edge in D=2, 3 and 4-dimensional lattices. The surface magnetization exponents are found to be: x_s=1.60(2), 2.65(15) and 3.7(1) in D=2, 3 and 4, respectively, which do not depend on the form of disorder. We have also studied critical magnetization profiles in slab, pyramid and wedge geometries with fixed-free boundary conditions and analyzed their scaling behavior.Comment: 7 pages, 11 figure

Random transverse-field Ising chain with long-range interactions

We study the low-energy properties of the long-range random transverse-field Ising chain with ferromagnetic interactions decaying as a power alpha of the distance. Using variants of the strong-disorder renormalization group method, the critical behavior is found to be controlled by a strong-disorder fixed point with a finite dynamical exponent z_c=alpha. Approaching the critical point, the correlation length diverges exponentially. In the critical point, the magnetization shows an alpha-independent logarithmic finite-size scaling and the entanglement entropy satisfies the area law. These observations are argued to hold for other systems with long-range interactions, even in higher dimensions.Comment: 6 pages, 4 figure

Corner contribution to percolation cluster numbers

We study the number of clusters in two-dimensional (2d) critical percolation, N_Gamma, which intersect a given subset of bonds, Gamma. In the simplest case, when Gamma is a simple closed curve, N_Gamma is related to the entanglement entropy of the critical diluted quantum Ising model, in which Gamma represents the boundary between the subsystem and the environment. Due to corners in Gamma there are universal logarithmic corrections to N_Gamma, which are calculated in the continuum limit through conformal invariance, making use of the Cardy-Peschel formula. The exact formulas are confirmed by large scale Monte Carlo simulations. These results are extended to anisotropic percolation where they confirm a result of discrete holomorphicity.Comment: 7 pages, 9 figure

From fracture to fragmentation: discrete element modeling -- Complexity of crackling noise and fragmentation phenomena revealed by discrete element simulations

Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack ensembles to the rapid fragmentation of materials DEM had a substantial contribution to our understanding over the past decades. Recently, the combination of DEM with other simulation techniques like Finite Element Modelling further extended the field of applicability. In this paper we briefly review the motivations and basic idea behind the DEM approach to cohesive particulate matter and then we give an overview of on-going developments and applications of the method focusing on two fields where recent success has been achieved. We discuss current challenges of this rapidly evolving field and outline possible future perspectives and debates

Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit

We consider the random-bond Potts model in the large-$Q$ limit and calculate the excess entropy, $S_{\Gamma}$, of a contour, $\Gamma$, which is given by the mean number of Fortuin-Kasteleyn clusters which are crossed by $\Gamma$. In two dimensions $S_{\Gamma}$ is proportional to the length of $\Gamma$, to which - at the critical point - there are universal logarithmic corrections due to corners. These are calculated by applying techniques of conformal field theory and compared with the results of large scale numerical calculations. The central charge of the model is obtained from the corner contributions to the excess entropy and independently from the finite-size correction of the free-energy as: $\lim_{Q \to \infty}c(Q)/\ln Q =0.74(2)$, close to previous estimates calculated at finite values of $Q$.Comment: 6 pages, 7 figure

Entanglement between random and clean quantum spin chains

The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being critical. In the composite, antiferromagnetic XX-chain with a sharp interface, the entropy is found to grow in a double-logarithmic fashion ${\cal S}\sim \ln\ln(L)$, where $L$ is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance $l$ from the contact point as $\sim l^{-\kappa}$. For $\kappa<1/2$, the entropy scales as ${\cal S}(\kappa) \simeq (1-2\kappa){\cal S}(\kappa=0)$, while for $\kappa \ge 1/2$, when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.Comment: 12 pages, 7 figures, Invited contribution to the Festschrift of John Cardy's 70th birthda

Development of Myxobolus dispar (Myxosporea : Myxobolidae) in an oligochaete alternate host, Tubifex tubifex

The development of Myxobolus dispar Thelohan, 1895, a myxosporean parasite of the gills of common carp (Cyprinus carpio L.) was studied in experimentally infected oligochaetes Tubifex tubifex Muller. After infection of uninfected tubificids with mature spores of M. dispar development of actinosporean stages was first observed light microscopically 21 days after initial exposure. In histological sections, early pansporocysts were located in the gut epithelium of experimental oligochaetes, while advanced stages occupied mostly the outer layers of the gut and the coelozoic space. Mature pansporocysts, each containing 8 raabeia spores, appeared 199 days after initial exposure. Following damage of the intestinal wall and rupture of the pansporocysts, free actinosporean stages were found in the gut lumen of the oligochaetes. Actinospores of M. dispar emerged from the worms after 217 days of intra-oligochaete development. They were floating in the water and showed a unique raabeia form. Each raabeia sport had three pyriform polar capsules and a cylindrical-shaped sporoplasm with approximately 32 secondary cells. The spore body joined the three caudal projections without a style. Caudal projections were bifurcated at the end and the two main branches had further small bifurcations. The total length of the raabeia sport was approximately 158 mu m. The prevalence of infection in 240 experimentally infected Tubifex specimens was 99.2%. No infection was found in the control oligochaetes

Comment on ``Magnetoresistance Anomalies in Antiferromagnetic YBa2_2Cu3_3O6+x_{6+x}: Fingerprints of Charged Stripes''

In a recent Letter Ando et al (cond-mat/9905071) discovered an anomalous magnetoresistance(MR) in hole doped antiferromagnetic YBa$_2$Cu$_3$O$_{6+x}$, which they attributed to charged stripes, i.e., to segregation of holes into lines. In this Comment we show that the experiments, albeit being interesting, do not prove the existence of stripes. In our view the anomalous behavior is due to an (a,b) plane anisotropy of the resistivity in the bulk and to a magnetic field dependent antiferromagnetic (AF) domain structure. It is unlikely that domain walls are charged stripes.Comment: 1 page, Accepted to PRL, Reply exists by authors of original pape