On the Aizenman exponent in critical percolation

The probabilities of clusters spanning a hypercube of dimensions two to seven along one axis of a percolation system under criticality were investigated numerically. We used a modified Hoshen--Kopelman algorithm combined with Grassberger's "go with the winner" strategy for the site percolation. We carried out a finite-size analysis of the data and found that the probabilities confirm Aizenman's proposal of the multiplicity exponent for dimensions three to five. A crossover to the mean-field behavior around the upper critical dimension is also discussed.Comment: 5 pages, 4 figures, 4 table

The RANLUX generator: resonances in a random walk test

Using a recently proposed directed random walk test, we systematically investigate the popular random number generator RANLUX developed by Luescher and implemented by James. We confirm the good quality of this generator with the recommended luxury level. At a smaller luxury level (for instance equal to 1) resonances are observed in the random walk test. We also find that the lagged Fibonacci and Subtract-with-Carry recipes exhibit similar failures in the random walk test. A revised analysis of the corresponding dynamical systems leads to the observation of resonances in the eigenvalues of Jacobi matrix.Comment: 18 pages with 14 figures, Essential addings in the Abstract onl

The interaction between education institution and employers in the process of preporation of experts

В статье приводится опыт организации взаимодействия субъектов рынка образовательных услуг – учреждений образования и рынка труда – представителей работодателей в процессе подготовки банковских специалистов.The article represents the experience of the interaction between the subjects of the market of educational services such as educational institutions and the labor market- employers in the process of professional training of banking specialists

The Cluster Processor: New Results

We present a progress report on the Cluster Processor, a special-purpose computer system for the Wolff simulation of the three-dimensional Ising model, including an analysis of simulation results obtained thus far. These results allow, within narrow error margins, a determination of the parameters describing the phase transition of the simple-cubic Ising model and its universality class. For an improved determination of the correction-to-scaling exponent, we include Monte Carlo data for systems with nearest-neighbor and third-neighbor interactions in the analysis.Comment: 14 pages, latex2

The critical amplitude ratio of the susceptibility in the random-site two-dimensional Ising model

We present a new way of probing the universality class of the site-diluted two-dimensional Ising model. We analyse Monte Carlo data for the magnetic susceptibility, introducing a new fitting procedure in the critical region applicable even for a single sample with quenched disorder. This gives us the possibility to fit simultaneously the critical exponent, the critical amplitude and the sample dependent pseudo-critical temperature. The critical amplitude ratio of the magnetic susceptibility is seen to be independent of the concentration $q$ of the empty sites for all investigated values of $q\le 0.25$. At the same time the average effective exponent $\gamma_{eff}$ is found to vary with the concentration $q$, which may be argued to be due to logarithmic corrections to the power law of the pure system. This corrections are canceled in the susceptibility amplitude ratio as predicted by theory. The central charge of the corresponding field theory was computed and compared well with the theoretical predictions.Comment: 6 pages, 4 figure