The Anderson transition: time reversal symmetry and universality

We report a finite size scaling study of the Anderson transition. Different scaling functions and different values for the critical exponent have been found, consistent with the existence of the orthogonal and unitary universality classes which occur in the field theory description of the transition. The critical conductance distribution at the Anderson transition has also been investigated and different distributions for the orthogonal and unitary classes obtained.Comment: To appear in Physical Review Letters. Latex 4 pages with 4 figure

One-parameter Superscaling at the Metal-Insulator Transition in Three Dimensions

Based on the spectral statistics obtained in numerical simulations on three dimensional disordered systems within the tight--binding approximation, a new superuniversal scaling relation is presented that allows us to collapse data for the orthogonal, unitary and symplectic symmetry ($\beta=1,2,4$) onto a single scaling curve. This relation provides a strong evidence for one-parameter scaling existing in these systems which exhibit a second order phase transition. As a result a possible one-parameter family of spacing distribution functions, $P_g(s)$, is given for each symmetry class $\beta$, where $g$ is the dimensionless conductance.Comment: 4 pages in PS including 3 figure

Metal-insulator transition in three dimensional Anderson model: universal scaling of higher Lyapunov exponents

Numerical studies of the Anderson transition are based on the finite-size scaling analysis of the smallest positive Lyapunov exponent. We prove numerically that the same scaling holds also for higher Lyapunov exponents. This scaling supports the hypothesis of the one-parameter scaling of the conductance distribution. From the collected numerical data for quasi one dimensional systems up to the system size 24 x 24 x infinity we found the critical disorder 16.50 < Wc < 16.53 and the critical exponent 1.50 < \nu < 1.54. Finite-size effects and the role of irrelevant scaling parameters are discussed.Comment: 4 pages, 2 figure

Anderson transitions in three-dimensional disordered systems with randomly varying magnetic flux

The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are considered. We find a critical exponent of $\nu=1.45\pm0.09$ with random scalar potential. Without it, $\nu$ is smaller but increases with the system size and extrapolates within the error bars to a value close to the above. The present results support the conventional classification of universality classes due to symmetry.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

Does a magnetic field modify the critical behaviour at the metal-insulator transition in 3-dimensional disordered systems?

The critical behaviour of 3-dimensional disordered systems with magnetic field is investigated by analyzing the spectral fluctuations of the energy spectrum. We show that in the thermodynamic limit we have two different regimes, one for the metallic side and one for the insulating side with different level statistics. The third statistics which occurs only exactly at the critical point is {\it independent} of the magnetic field. The critical behaviour which is determined by the symmetry of the system {\it at} the critical point should therefore be independent of the magnetic field.Comment: 10 pages, Revtex, 4 PostScript figures in uuencoded compressed tar file are appende

Anderson transition in three-dimensional disordered systems with symplectic symmetry

The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent $\nu$ of the localization length is extracted and estimated to be $\nu = 1.3 \pm 0.2$. The level statistics at the critical point are also analyzed and shown to be scale independent. The form of the energy level spacing distribution $P(s)$ at the critical point is found to be different from that for the orthogonal ensemble suggesting that the breaking of spin rotation symmetry is relevant at the critical point.Comment: 4 pages, revtex, to appear in Physical Review Letters. 3 figures available on request either by fax or normal mail from [email protected] or [email protected]

Phase diagram of localization in a magnetic field

The phase diagram of localization is numerically calculated for a three-dimensional disordered system in the presence of a magnetic field using the Peierls substitution. The mobility edge trajectory shifts in the energy-disorder space when increasing the field. In the band center, localized states near the phase boundary become delocalized. The obtained field dependence of the critical disorder is in agreement with a power law behavior expected from scaling theory. Close to the tail of the band the magnetic field causes localization of extended states.Comment: 4 pages, RevTeX, 3 PS-figures (4 extra references are included, minor additions), to appear in Phys. Rev. B as a Brief Repor

Anomalous diffusion at the Anderson transitions

Diffusion of electrons in three dimensional disordered systems is investigated numerically for all the three universality classes, namely, orthogonal, unitary and symplectic ensembles. The second moment of the wave packet $$ at the Anderson transition is shown to behave as $\sim t^a (a\approx 2/3)$. From the temporal autocorrelation function $C(t)$, the fractal dimension $D_2$ is deduced, which is almost half the value of space dimension for all the universality classes.Comment: Revtex, 2 figures, to appear in J. Phys. Soc. Jpn.(1997) Fe

Electrical properties of isotopically enriched neutron-transmutation-doped ^{70} Ge:Ga near the metal-insulator transition

We report the low temperature carrier transport properties of a series of nominally uncompensated neutron-transmutation doped (NTD) ^{70} Ge:Ga samples very close to the critical concentration N_c for the metal-insulator transition. The concentration of the sample closest to N_c is 1.0004N_c and it is unambiguously shown that the critical conductivity exponent is 0.5. Properties of insulating samples are discussed in the context of Efros and Shklovskii's variable range hopping conduction.Comment: 8 pages using REVTeX, 8 figures, published versio

Reliability of an injury scoring system for horses

<p>Abstract</p> <p>Background</p> <p>The risk of injuries is of major concern when keeping horses in groups and there is a need for a system to record external injuries in a standardised and simple way. The objective of this study, therefore, was to develop and validate a system for injury recording in horses and to test its reliability and feasibility under field conditions.</p> <p>Methods</p> <p>Injuries were classified into five categories according to severity. The scoring system was tested for intra- and inter-observer agreement as well as agreement with a 'golden standard' (diagnosis established by a veterinarian). The scoring was done by 43 agricultural students who classified 40 photographs presented to them twice in a random order, 10 days apart. Attribute agreement analysis was performed using Kendall's coefficient of concordance (Kendall's <it>W</it>), Kendall's correlation coefficient (Kendall's τ) and Fleiss' kappa. The system was also tested on a sample of 100 horses kept in groups where injury location was recorded as well.</p> <p>Results</p> <p>Intra-observer agreement showed Kendall's <it>W </it>ranging from 0.94 to 0.99 and 86% of observers had kappa values above 0.66 (substantial agreement). Inter-observer agreement had an overall Kendall's <it>W </it>of 0.91 and the mean kappa value was 0.59 (moderate). Agreement for all observers versus the 'golden standard' had Kendall's τ of 0.88 and the mean kappa value was 0.66 (substantial). The system was easy to use for trained persons under field conditions. Injuries of the more serious categories were not found in the field trial.</p> <p>Conclusion</p> <p>The proposed injury scoring system is easy to learn and use also for people without a veterinary education, it shows high reliability, and it is clinically useful. The injury scoring system could be a valuable tool in future clinical and epidemiological studies.</p