Distribution of averages in a correlated Gaussian medium as a tool for the estimation of the cluster distribution on size

Calculation of the distribution of the average value of a Gaussian random field in a finite domain is carried out for different cases. The results of the calculation demonstrate a strong dependence of the width of the distribution on the spatial correlations of the field. Comparison with the simulation results for the distribution of the size of the cluster indicates that the distribution of an average field could serve as a useful tool for the estimation of the asymptotic behavior of the distribution of the size of the clusters for "deep" clusters where value of the field on each site is much greater than the rms disorder.Comment: 15 pages, 6 figures, RevTe

Droplets in the coexistence region of the two-dimensional Ising model

The two-dimensional Ising model with fixed magnetization is studied using Monte Carlo techniques. At the coexistence line, the macroscopic, extensive droplet of minority spins becomes thermally unstable by breaking up into microscopic clusters. Intriguing finite--size effects as well as singularities of thermal and cluster properties associated with the transition are discussed.Comment: 7 pages, 3 figures included, submitted to J. Phys. A: Math. Ge

Percolation-to-hopping crossover in conductor-insulator composites

Here, we show that the conductivity of conductor-insulator composites in which electrons can tunnel from each conducting particle to all others may display both percolation and tunneling (i.e. hopping) regimes depending on few characteristics of the composite. Specifically, we find that the relevant parameters that give rise to one regime or the other are $D/\xi$ (where $D$ is the size of the conducting particles and $\xi$ is the tunneling length) and the specific composite microstructure. For large values of $D/\xi$, percolation arises when the composite microstructure can be modeled as a regular lattice that is fractionally occupied by conducting particle, while the tunneling regime is always obtained for equilibrium distributions of conducting particles in a continuum insulating matrix. As $D/\xi$ decreases the percolating behavior of the conductivity of lattice-like composites gradually crosses over to the tunneling-like regime characterizing particle dispersions in the continuum. For $D/\xi$ values lower than $D/\xi\simeq 5$ the conductivity has tunneling-like behavior independent of the specific microstructure of the composite.Comment: 8 pages, 5 figure

Non-Markovian Persistence and Nonequilibrium Critical Dynamics

The persistence exponent \theta for the global order parameter, M(t), of a system quenched from the disordered phase to its critical point describes the probability, p(t) \sim t^{-\theta}, that M(t) does not change sign in the time interval t following the quench. We calculate \theta to O(\epsilon^2) for model A of critical dynamics (and to order \epsilon for model C) and show that at this order M(t) is a non-Markov process. Consequently, \theta is a new exponent. The calculation is performed by expanding around a Markov process, using a simplified version of the perturbation theory recently introduced by Majumdar and Sire [Phys. Rev. Lett. _77_, 1420 (1996); cond-mat/9604151].Comment: 4 pages, Revtex, no figures, requires multicol.st

Persistence Probabilities of the German DAX and Shanghai Index

We present a relatively detailed analysis of the persistence probability distributions in financial dynamics. Compared with the auto-correlation function, the persistence probability distributions describe dynamic correlations non-local in time. Universal and non-universal behaviors of the German DAX and Shanghai Index are analyzed, and numerical simulations of some microscopic models are also performed. Around the fixed point $z_0=0$, the interacting herding model produces the scaling behavior of the real markets

Connected component identification and cluster update on GPU

Cluster identification tasks occur in a multitude of contexts in physics and engineering such as, for instance, cluster algorithms for simulating spin models, percolation simulations, segmentation problems in image processing, or network analysis. While it has been shown that graphics processing units (GPUs) can result in speedups of two to three orders of magnitude as compared to serial codes on CPUs for the case of local and thus naturally parallelized problems such as single-spin flip update simulations of spin models, the situation is considerably more complicated for the non-local problem of cluster or connected component identification. I discuss the suitability of different approaches of parallelization of cluster labeling and cluster update algorithms for calculations on GPU and compare to the performance of serial implementations.Comment: 15 pages, 14 figures, one table, submitted to PR

Lattice dynamics of mixed semiconductors (Be,Zn)Se from first-principles calculations

Vibration properties of Zn(1-x)Be(x)Se, a mixed II-VI semiconductor haracterized by a high contrast in elastic properties of its pure constituents, ZnSe and BeSe, are simulated by first-principles calculations of electronic structure, lattice relaxation and frozen phonons. The calculations within the local density approximation has been done with the Siesta method, using norm-conserving pseudopotentials and localized basis functions; the benchmark calculations for pure endsystems were moreover done also by all-electron WIEN2k code. An immediate motivation for the study was to analyze, at the microscopic level, the appearance of anomalous phonon modes early detected in Raman spectra in the intermediate region (20 to 80%) of ZnBe concentration. This was early discussed on the basis of a percolation phenomenon, i.e., the result of the formation of wall-to-wall --Be--Se-- chains throughout the crystal. The presence of such chains was explicitly allowed in our simulation and indeed brought about a softening and splitting off of particular modes, in accordance with experimental observation, due to a relative elongation of Be--Se bonds along the chain as compared to those involving isolated Be atoms. The variation of force constants with interatomic distances shows common trends in relative independence on the short-range order.Comment: 11 pages, 10 figures, to be published in Phys. Rev.

Critical exponents and phase transition in gold nuclei fragmentation at energies 10.6 and 4.0 GeV/nucleon

An attempt to extract critical exponents gamma, beta and tau from data on gold nuclei fragmentation due to interactions with nuclear emulsion at energies 4.0 A GeV and 10.6 A GeV is presented. Based on analysis of Campi's 2nd charge moments, two subsets of data at each energy are selected from the inclusive data, corresponding to 'liquid' and 'gas' phases. The extracted values of critical exponents from the selected data sets are in agreement with predictions of 'liquid-gas' model of phase transition.Comment: 21 pages, 15 figure

High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions

In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the \sus and the free energy are obtained for the quenched bond-diluted Ising model in $d = 3$--5 dimensions. They are analysed using different extrapolation methods tailored to the expected singularity behaviours. In $d = 4$ and 5 dimensions we confirm that the critical behaviour is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in $d = 4$ is confirmed and our results for the critical behaviour of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation and random fixed point. We estimate the critical exponent of the \sus to be $\gamma =1.305(5)$ at the random fixed point.Comment: 16 pages, 10 figure