Related papers: Reply to Suslov
In a recent publication, J. Phys.: Condens. Matt. 14 13777 (2002), Kuzovkov et. al. announced an analytical solution of the two-dimensional Anderson localisation problem via the calculation of a generalised Lyapunov exponent using signal…
We calculate the critical amplitudes of the Polyakov loop and its susceptibility at the deconfinement transition of (3+1) dimensional SU(2) gauge theory. To this end we study the corrections due to irrelevant exponents in the scaling…
This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are…
Our recent Monte Carlo results [Phys. Rev. E 61 (2000) 6330] for the one-dimensional reaction-diffusion process A+B->2B and B->A lead to the correlation length exponent estimate nu=2.21 +/- 0.05. In a comment on our work [cond-mat/0007366]…
Disordered non-interacting systems are classified into ten symmetry classes, with the unitary class being the most fundamental. The three and four dimensional unitary universality classes are attracting renewed interest because of their…
We reconcile the phenomenon of mesoscopic conductance fluctuations with the single parameter scaling theory of the Anderson transition. We calculate three averages of the conductance distribution: $\exp(<\ln g>)$, $<g>$ and $1/<R>$ where…
The distribution of energy level separations for lattices of sizes up to 28$\times$28$\times$28 sites is numerically calculated for the Anderson model. The results show one-parameter scaling. The size-independent universality of the…
The use of a new method for summing divergent series makes it possible to significantly increase the accuracy of determining the critical exponents from the field theoretical renormalization group. The exponent value \nu=0.6700\pm 0.0006…
The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is…
We study the Anderson-type transition previously found in the spectrum of the QCD quark Dirac operator in the high temperature, quark-gluon plasma phase. Using finite size scaling for the unfolded level spacing distribution, we show that in…
The Gaussian transition in the spin-one Heisenberg chain with single-ion anisotropy is extremely difficult to treat, both analytically and numerically. We introduce an improved DMRG procedure with strict error control, which we use to…
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…
The wavefunction statistics at the Anderson transition in a 2d disordered electron gas with spin-orbit coupling is studied numerically. In addition to highly accurate exponents ($\alpha_0{=}2.172\pm 0.002, \tau_2{=}1.642\pm 0.004$), we…
The critical temperature of thin Fe layers on Ir(100) is measured through M\"o{\ss}bauer spectroscopy as a function of the layer thickness. From a phenomenological finite-size scaling analysis, we find an effective shift exponent lambda =…
Using the Anderson model for disordered systems the fluctuations in electron spectra near the metal--insulator transition were numerically calculated for lattices of sizes up to 28 x 28 x 28 sites. The results show a finite--size scaling of…
Pseudo-$\epsilon$ expansions ($\tau$-series) for critical exponents of 3D XY model describing $\lambda$-transition in liquid helium are derived up to $\tau^6$ terms. Numerical estimates extracted from the $\tau$-series obtained using…
In this paper we analyze the predictions of the forward approximation in some models which exhibit an Anderson (single-) or many-body localized phase. This approximation, which consists in summing over the amplitudes of only the shortest…
An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that…
Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance…
We calculate the critical amplitudes of the Polyakov loop and its susceptibility at the deconfinement transition of SU(2) gauge theory. To this end we carefully study the corrections to the scaling functions of the observables coming from…