Critical Point Correlation Function for the 2D Random Bond Ising Model

High accuracy Monte Carlo simulation results for 1024*1024 Ising system with ferromagnetic impurity bonds are presented. Spin-spin correlation function at a critical point is found to be numerically very close to that of a pure system. This is not trivial since a critical temperature for the system with impurities is almost two times lower than pure Ising $T_c$. Finite corrections to the correlation function due to combined action of impurities and finite lattice size are described.Comment: 7 pages, 2 figures after LaTeX fil

Cardiorenal syndrome in the early stages of coronary bypass surgery

Aim: evaluate the frequency and risk factors of postoperative atrial fibrillation (pAF) in patients with chronic coronary artery disease (CHD) with acute kidney injury (AKI) developed in connection with coronary artery bypass grafting (CABG). Materials and methods. The study involved 90 patients (pts) undergoing CABG at age 58±7 years, duration of CHD - 6±6 years. 80% of pts had previous myocardial infarction. Chronic heart failure, functional class II was detected in 53.3% pts, functional class III - in 46.7% pts. Multi-vessel coronary lesions had 75.6% pts. CABG with cardiopulmonary bypass was performed in 88.9% pts, operation on a beating heart was fulfilled in 11.1% pts. Creatinine was determined by Jaffe method, the glomerular filtration rate (GFR) was calculated with the СКD-EPI formula. AKI was diagnosed according to KDIGO criteria, 2012. Results and discussion. The frequency of transient AKI after CABG was 33.3%, pAF - 17.8 %, pAF among those with AKI was 20%. The development of AKI was associated with higher levels of troponin T after CABG (Me [25; 75 percentiles] - 0.36 [0.24; 0.99] versus 0.28 [0.11; 0.50] ng/ml; p=0.037), with more frequent use of inotropic drugs (60% and 25%; p=0.002), longer duration of inotropic therapy (2.0 [1.0; 2.5] versus 1.0 [0; 1.0] days; p=0.001). The proportion of patients who had pAF among those with AKI and without it were not significantly different (20% and 16.7%; p=0.7). Decrease in GFR less than 39 [29.8; 45.7] ml/min/1.73 m2 after CABG was the most important risk factor of pAF in pts with CHD and AKI

Critical region of the random bond Ising model

We describe results of the cluster algorithm Special Purpose Processor simulations of the 2D Ising model with impurity bonds. Use of large lattices, with the number of spins up to $10^6$, permitted to define critical region of temperatures, where both finite size corrections and corrections to scaling are small. High accuracy data unambiguously show increase of magnetization and magnetic susceptibility effective exponents $\beta$ and $\gamma$, caused by impurities. The $M$ and $\chi$ singularities became more sharp, while the specific heat singularity is smoothed. The specific heat is found to be in a good agreement with Dotsenko-Dotsenko theoretical predictions in the whole critical range of temperatures.Comment: 11 pages, 16 figures (674 KB) by request to authors: [email protected] or [email protected], LITP-94/CP-0

The stability of a cubic fixed point in three dimensions from the renormalization group

The global structure of the renormalization-group flows of a model with isotropic and cubic interactions is studied using the massive field theory directly in three dimensions. The four-loop expansions of the \bt-functions are calculated for arbitrary $N$. The critical dimensionality $N_c=2.89 \pm 0.02$ and the stability matrix eigenvalues estimates obtained on the basis of the generalized Pad$\acute{\rm e}$-Borel-Leroy resummation technique are shown to be in a good agreement with those found recently by exploiting the five-loop \ve-expansions.Comment: 18 pages, LaTeX, 5 PostScript figure

Weak quenched disorder and criticality: resummation of asymptotic(?) series

In these lectures, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range-correlated random-site disorder, and (iii) random anisotropy. Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of these lectures is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.Comment: Lectures given at the Second International Pamporovo Workshop on Cooperative Phenomena in Condensed Matter (28th July - 7th August 2001, Pamporovo, Bulgaria). 51 pages, 12 figures, 1 style files include

Critical behavior of weakly-disordered anisotropic systems in two dimensions

The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin-Teller model (GATM) is studied. In the critical region this model is shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large distance behavior of the two-spin correlation function. The equation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same universality class as that of the two-dimensional Ising model. The critical exponent $\nu$ of the correlation length for the 3- and 4-state random-bond Potts models is also calculated in a 3-loop approximation. We show that this exponent is given by an apparently convergent series in $\epsilon=c-\frac{1}{2}$ (with $c$ the central charge of the Potts model) and that the numerical values of $\nu$ are very close to that of the 2D Ising model. This work therefore supports the conjecture (valid only approximately for the 3- and 4-state Potts models) of a superuniversality for the 2D disordered models with discrete symmetries.Comment: REVTeX, 24 pages, to appear in Phys.Rev.

Light scattering by an ensemble of interacting dipolar particles with both electric and magnetic polarizabilities

We have studied the problem of light scattering by an ensemble of dipoles with both electric and magnetic polarizabilities. Using the coupled electric and magnetic dipole method as the formal base, we have generalized the eigenvector decomposition of the local dipole moments previously derived for purely electric particles to the case of both electric and magnetic dipoles. We have analyzed the properties of eigenvalues and eigenvectors in the most elementary case of two particles. In the purely electric case, the eigenvalues correspond to the resonance modes of the system due to the electromagnetic coupling of its components. For a two-dipole system with both electric and magnetic responses, purely electric, purely magnetic, and mixed states can be distinguished. The resonance spectrum is analyzed as a function of the magnetic permeability, and it is shown that the latter can be fitted quite accurately by the eigenmode decomposition

On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet

We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin correlation functions (from which averaged correlation lengths, $\xi^{ave}$, are computed) by transfer-matrix methods. An {\it ansatz} for the size-dependence of logarithmic corrections to $\xi^{ave}$ is proposed. Data for both random-bond and site-diluted systems show that pure system behaviour (with $\nu=1$) is recovered if these corrections are incorporated, discarding the weak--universality scenario.Comment: RevTeX code, 4 pages plus 2 Postscript figures; to appear in Physical Review B Rapid Communication

The two-dimensional random-bond Ising model, free fermions and the network model

We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a localisation problem belonging to one of a set of non-standard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalisation transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width $M$ is proportional to $M^{3}$, and not exponential in $M$ as with conventional algorithms. We show how the approach may be used to calculate for the RBIM: the free energy; typical correlation lengths in quasi-one dimension for both the spin and the disorder operators; even powers of spin-spin correlation functions and their disorder-averages. We examine in detail the square-lattice, nearest-neighbour $\pm J$ RBIM, in which bonds are independently antiferromagnetic with probability $p$, and ferromagnetic with probability $1-p$. Studying temperatures $T\geq 0.4J$, we obtain precise coordinates in the $p-T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small $p$, and determine critical exponents at the multicritical point.Comment: 20 pages, 25 figures, figures correcte

Enhanced He-alpha emission from "smoked" Ti targets irradiated with 400nm, 45 fs laser pulses

We present a study of He-like 1s(2)-1s2p line emission from solid and low-density Ti targets under similar or equal to 45 fs laser pulse irradiation with a frequency doubled Ti: Sapphire laser. By varying the beam spot, the intensity on target was varied from 10(15) W/cm(2) to 10(19) W/cm(2). At best focus, low density "smoked" Ti targets yield similar to 20 times more He-alpha than the foil targets when irradiated at an angle of 45 degrees with s-polarized pulses. The duration of He-alpha emission from smoked targets, measured with a fast streak camera, was similar to that from Ti foils