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We review recent advances in the analysis of the Wang--Landau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random walk in the energy space biased with the Wang-Landau probability. Properties of the TMES can explain some features of the Wang-Landau algorithm, for example, the flatness of the histogram. We show that the Wang--Landau probability with the true DOS generates a Markov process in the energy space and the inverse spectral gap of the TMES can estimate the mixing time of this Markov process. We argue that an efficient implementation of the Wang-Landau algorithm consists of two simulation stages: the original Wang-Landau procedure for the first stage and a $1/t$ modification for the second stage. The mixing time determines the characteristic time for convergence to the true DOS in the second simulation stage. The parameter of the convergence of the estimated DOS to the true DOS is the difference of the largest TMES eigenvalue from unity. The characteristic time of the first stage is the tunneling time, i.e., the time needed for the system to visit all energy levels., Comment: 31st Annual Worskshop "Recent Developments in Computer Simulational Studies in Condensed Matter Physics", Center for Simulational Physics, University of Georgia, February 19-23, 2018

The Wang-Landau (WL) algorithm has been widely used for simulations in many areas of physics. Our analysis of the WL algorithm explains its properties and shows that the difference of the largest eigenvalue of the transition matrix in the energy space from unity can be used to control the accuracy of estimating the density of states. Analytic expressions for the matrix elements are given in the case of the one-dimensional Ising model. The proposed method is further confirmed by numerical results for the one-dimensional and two-dimensional Ising models and also the two-dimensional Potts model., Comment: 8 pages, 6 figures

We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) $q$-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, the critical behavior, including corrections to scaling, are analyzed. The role of randomness is scrutinized. Results are discussed applying scaling arguments and invoking findings for bulk critical properties. In all studied cases, i.e., $q = 3$, $4$, and $q = 8$, the spread of the interfacial adsorption profiles is observed to increase linearly with the lattice size at the bulk transition point., Comment: 6 pages, 6 eps figures, 1 table, minor corrections, accepted for publication in Eur. Phys. J. B

In this update, we present the new version of the random number generator (RNG) library RNGSSELIB, which, in particular, contains fast SSE realizations of a number of modern and most reliable generators \cite{RNGSSELIB1}. The new features are: i) Fortran compatibility and examples of using the library in Fortran; ii) new modern and reliable generators; iii) the abilities to jump ahead inside RNG sequence and to initialize up to $10^{19}$ independent random number streams with block splitting method., Comment: 6 pages, 1 table

The library PRAND for pseudorandom number generation for modern CPUs and GPUs is presented. It contains both single-threaded and multi-threaded realizations of a number of modern and most reliable generators recently proposed and studied in [1,2,3,4,5] and the efficient SIMD realizations proposed in [6]. One of the useful features for using PRAND in parallel simulations is the ability to initialize up to $10^{19}$ independent streams. Using massive parallelism of modern GPUs and SIMD parallelism of modern CPUs substantially improves performance of the generators., Comment: 29 pages, 1 figure, 7 tables

Several dynamical stages of the Marangoni convection of an evaporating sessile drop are obtained. We jointly take into account the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the drop and the diffusion of vapor in air. The stages are characterized by different number of vortices in the drop and the spatial location of vortices. During the early stage the array of vortices arises near a surface of the drop and induces a non-monotonic spatial distribution of the temperature over the drop surface. The number of near-surface vortices in the drop is controlled by the Marangoni cell size, which is calculated similar to that given by Pearson for flat fluid layers. The number of vortices quickly decreases with time, resulting in three bulk vortices in the intermediate stage. The vortex structure finally evolves into the single convection vortex in the drop, existing during about 1/2 of the evaporation time., Comment: 5 pages, 3 figures, conference CCP2010

The library RNGSSELIB for random number generators (RNGs) based upon the SSE2 command set is presented. The library contains realization of a number of modern and most reliable generators. Usage of SSE2 command set allows to substantially improve performance of the generators. Three new RNG realizations are also constructed. We present detailed analysis of the speed depending on compiler usage and associated optimization level, as well as results of extensive statistical testing for all generators using available test packages. Fast SSE implementations produce exactly the same output sequence as the original algorithms., Comment: 15 pages

The Binder cumulant at the phase transition of Ising models on square lattices with ferromagnetic couplings between nearest neighbors and with competing antiferromagnetic couplings between next--nearest neighbors, along only one diagonal, is determined using Monte Carlo techniques. In the phase diagram a disorder line occurs separating regions with monotonically decaying and with oscillatory spin--spin correlations. Findings on the variation of the critical cumulant with the ratio of the two interaction strengths are compared to related recent results based on renormalization group calculations., Comment: 4 pages, 4 figures

Theoretical description and numerical simulation of an evaporating sessile drop are developed. We jointly take into account the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the drop and the diffusion of vapor in air. A shape of the rotationally symmetric drop is determined within the quasistationary approximation. Nonstationary effects in the diffusion of the vapor are also taken into account. Simulation results agree well with the data of evaporation rate measurements for the toluene drop. Marangoni forces associated with the temperature dependence of the surface tension, generate fluid convection in the sessile drop. Our results demonstrate several dynamical stages of the convection characterized by different number of vortices in the drop. During the early stage the street of vortices arises near a surface of the drop and induces a non-monotonic spatial distribution of the temperature over the drop surface. The initial number of near-surface vortices in the drop is controlled by the Marangoni cell size which is similar to that given by Pearson for flat fluid layers. This number quickly decreases with time, resulting in three bulk vortices in the intermediate stage. The vortices finally transform into the single convection vortex in the drop, existing during about 1/2 of the evaporation time., Comment: 23 pages, 12 figures

A state of an electron in a quantum wire or a thin film becomes metastable, when a static electric field is applied perpendicular to the wire direction or the film surface. The state decays via tunneling through the created potential barrier. An additionally applied magnetic field, perpendicular to the electric field, can increase the tunneling decay rate for many orders of magnitude. This happens, when the state in the wire or the film has a velocity perpendicular to the magnetic field. According to the cyclotron effect, the velocity rotates under the barrier and becomes more aligned with the direction of tunneling. This mechanism can be called cyclotron enhancement of tunneling.

We develop a technique for probing harmonic measure of the diffusion limited aggregation (DLA) cluster surface with the variable size particle and generate one thousand clusters with 50 million particles using original off-lattice killing-free algorithm. Taking, in sequence, the limit of the vanishing size of the probing particles and then sending the growing cluster size to infinity, we achieve the unprecedented accuracy determining the fractal dimension, D=1.7100(2) crucial to characterization of geometric properties of the DLA clusters., Comment: 4 pages, 5 figures

The Binder cumulant at the phase transition of Ising models on square lattices with various ferromagnetic nearest and next-nearest neighbour couplings is determined using mainly Monte Carlo techniques. We discuss the possibility to relate the value of the critical cumulant in the isotropic, nearest neighbour and in the anisotropic cases to each other by means of a scale transformation in rectangular geometry, to pinpoint universal and nonuniversal features., Comment: 7 pages, 4 figures, submitted to J. Phys. A

We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessary correlations are always present in practice. We show that introducing hidden variables and introducing rotation in the RNG output, accompanied with the proper initialization, dramatically suppress these correlations. We analyze the mechanisms of the single-cat-map correlations analytically and show how to diminish them. We generalize the Percival-Vivaldi theory in the case of the ensemble of maps, find the period of the proposed RNG analytically, and also analyze its properties. We present efficient practical realizations for the RNGs and check our predictions numerically. We also test our RNGs using the known stringent batteries of statistical tests and find that the statistical properties of our best generators are not worse than those of other best modern generators., Comment: 18 pages, 3 figures, 9 tables

We analyze the evolution of the local simulation times (LST) in Parallel Discrete Event Simulations. The new ingredients introduced are i) we associate the LST with the nodes and not with the processing elements, and 2) we propose to minimize the exchange of information between different processing elements by freezing the LST on the boundaries between processing elements for some time of processing and then releasing them by a wide-stream memory exchange between processing elements. Highlights of our approach are i) it keeps the highest level of processor time utilization during the algorithm evolution, ii) it takes a reasonable time for the memory exchange excluding the time-consuming and complicated process of message exchange between processors, and iii) the communication between processors is decoupled from the calculations performed on a processor. The effectiveness of our algorithm grows with the number of nodes (or threads). This algorithm should be applicable for any parallel simulation with short-range interactions, including parallel or grid simulations of partial differential equations., Comment: 24 pages with 11 figures

Using Monte Carlo techniques, the two-dimensional site-diluted Ising model is studied. In particular, properties of the specific heat, its critical behaviour and the emergence of a non-singular maximum above the transition temperature at moderate concentration of defects, are discussed., Comment: 10 pages, 5 eps-figures, elsart-style, submitted to Physica A

The probability of simultaneous occurence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice at the bond percolation threshold Pc=1/2. The calculated probabilities for free boundary conditions and periodic boundary conditions are in a very good coincidence with the exact formulae developed recently by Cardy., Comment: Contribution to Lattice 97, LaTeX, 3 pages, 4 figures (1-eps, 3- LaTeX)

We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in several types of pseudo-random-number sequences. This model provides qualitative understanding of the bias mechanism in a class of cluster Monte Carlo algorithms., Comment: 12 pages, LaTeX, elsart, epsf, to appear in Physica A