Related papers: Critical Exponent of the Anderson Transition using…
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling…
We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional…
We propose a new viewpoint on the study of localization transitions in disordered quantum systems, showing how critical properties can be seen also as a geometric transition in the data space generated by the classically encoded…
The level spacing distribution is numerically calculated at the disorder-induced metal--insulator transition for dimensionality d=4 by applying the Lanczos diagonalisation. The critical level statistics are shown to deviate stronger from…
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the…
Three-dimensional spin models of the Ising and XY universality classes are studied by a combination of high-temperature expansions and Monte Carlo simulations. Critical exponents are determined to very high precision. Scaling amplitude…
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…
We clarify universal critical properties of delocalization-localization transitions in three-dimensional (3D) unitary and orthogonal classes with particle-hole and/or chiral symmetries (classes AIII, BDI, D, C and CI). We first introduce…
In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…
We study the phase diagram and quantum critical region of one of the fundamental models for electronic correlations: the periodic Anderson model. Employing the recently developed dynamical vertex approximation, we find a phase transition…
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1<K\le 2$, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a…
Statistical model checking avoids the exponential growth of states associated with probabilistic model checking by estimating properties from multiple executions of a system and by giving results within confidence bounds. Rare properties…
In the absence of impurities and boundary effects, first order phase transitions are initiated by the nucleation of critical bubbles. In thermally driven transitions many systems can remain metastable for an extended time, possibly tens of…
A binary liquid near its consolute point exhibits critical fluctuations of the local composition; the diverging correlation length has always challenged simulations. The method of choice for the calculation of critical points in the phase…
The superconducting transition in presence of strong columnar disorder parallel to the magnetic field is considered. A solvable model appropriate for description of the broad crossover regime towards the true "glassy" critical behavior is…
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the…
We compute the number level variance $\Sigma_{2}$ and the level compressibility $\chi$ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the…
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…
A typical problem with Monte Carlo simulations in statistical physics is that they do not allow for a direct calculation of the free energy. For systems at criticality, this means that one cannot calculate the central charge in a Monte…
The corrections to finite-size scaling in the critical two-point correlation function G(r) of 2D Ising model on a square lattice have been studied numerically by means of exact transfer-matrix algorithms. The systems of square geometry with…