A new comprehensive study of the 3D random-field Ising model via sampling the density of states in dominant energy subspaces

The three-dimensional bimodal random-field Ising model is studied via a new finite temperature numerical approach. The methods of Wang-Landau sampling and broad histogram are implemented in a unified algorithm by using the N-fold version of the Wang-Landau algorithm. The simulations are performed in dominant energy subspaces, determined by the recently developed critical minimum energy subspace technique. The random fields are obtained from a bimodal distribution, that is we consider the discrete $(\pm\Delta)$ case and the model is studied on cubic lattices with sizes $4\leq L \leq 20$. In order to extract information for the relevant probability distributions of the specific heat and susceptibility peaks, large samples of random field realizations are generated. The general aspects of the model's scaling behavior are discussed and the process of averaging finite-size anomalies in random systems is re-examined under the prism of the lack of self-averaging of the specific heat and susceptibility of the model.Comment: 10 pages, 4 figures, presented at the third NEXT Sigma Phi International Conference, Kolymbari, Greece (2005

Wetting and interfacial adsorption in the Blume-Capel model on the square lattice

We study the Blume-Capel model on the square lattice. To allow for wetting and interfacial adsorption, the spins on opposite boundaries are fixed in two different states, "+1" and "-1", with reduced couplings at one of the boundaries. Using mainly Monte Carlo techniques, of Metropolis and Wang-Landau type, phase diagrams showing bulk and wetting transitions are determined. The role of the non-boundary state, "0", adsorbed preferably at the interface between "-1" and "+1" rich regions, is elucidated.Comment: 7 pages, 8 figures, minor corrections to previous versio

A study for the static properties of symmetric linear multiblock copolymers under poor solvent conditions

We use a standard bead-spring model and molecular dynamics simulations to study the static properties of symmetric linear multiblock copolymer chains and their blocks under poor solvent conditions in a dilute solution from the regime close to theta conditions, where the chains adopt a coil-like formation, to the poorer solvent regime where the chains collapse obtaining a globular formation and phase separation between the blocks occurs. We choose interaction parameters as is done for a standard model, i.e., the Lennard-Jones fluid and we consider symmetric chains, i.e., the multiblock copolymer consists of an even number $n$ of alternating chemically different A and B blocks of the same length $N_{A}=N_{B}=N$. We show how usual static properties of the individual blocks and the whole multiblock chain can reflect the phase behavior of such macromolecules. Also, how parameters, such as the number of blocks $n$ can affect properties of the individual blocks, when chains are in a poor solvent for a certain range of $n$. A detailed discussion of the static properties of these symmetric multiblock copolymers is also given. Our results in combination with recent simulation results on the behavior of multiblock copolymer chains provide a complete picture for the behavior of these macromolecules under poor solvent conditions, at least for this most symmetrical case. Due to the standard choice of our parameters, our system can be used as a benchmark for related models, which aim at capturing the basic aspects of the behavior of various biological systems.Comment: 13 pages, 11 figure

Geometry effects in the magnetoconductance of normal and Andreev Sinai billiards

We study the transport properties of low-energy (quasi)particles ballistically traversing normal and Andreev two-dimensional open cavities with a Sinai-billiard shape. We consider four different geometrical setups and focus on the dependence of transport on the strength of an applied magnetic field. By solving the classical equations of motion for each setup we calculate the magnetoconductance in terms of transmission and reflection coefficients for both the normal and Andreev versions of the billiard, calculating in the latter the critical field value above which the outgoing current of holes becomes zero.Comment: 4 pages, 4 figure

Universality aspects of the d=3 random-bond Blume-Capel model

The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that, the second-order transition emerging under bond randomness from the first-order regime of the pure model, belongs to a new and distinctive universality class. The first finding reinforces the scenario of a single universality class for the 3d Ising model with the three well-known types of quenched uncorrelated disorder (bond randomness, site- and bond-dilution). The second, amounts to a strong violation of universality principle of critical phenomena. For this case of the ex-first-order 3d Blume-Capel model, we find sharp differences from the critical behaviors, emerging under randomness, in the cases of the ex-first-order transitions of the corresponding weak and strong first-order transitions in the 3d three-state and four-state Potts models.Comment: 12 pages, 12 figure

Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals

In this communication, the convergence of the 1/t and Wang - Landau algorithms in the calculation of multidimensional numerical integrals is analyzed. Both simulation methods are applied to a wide variety of integrals without restrictions in one, two and higher dimensions. The errors between the exact and the calculated values of the integral are obtained and the efficiency and accuracy of the methods are determined by their dynamical behavior. The comparison between both methods and the simple sampling Monte Carlo method is also reported. It is observed that the time dependence of the errors calculated with 1/t algorithm goes as N^{-1/2} (with N the MC trials) in quantitative agreement with the simple sampling Monte Carlo method. It is also showed that the error for the Wang - Landau algorithm saturates in time evidencing the non-convergence of the methods. The sources for the error are also determined.Comment: 8 pages, 5 figure