Diffusion-limited aggregates grown on nonuniform substrates

In the present paper, patterns of diffusion-limited aggregation (DLA) grown on nonuniform substrates are investigated by means of Monte Carlo simulations. We consider a nonuniform substrate as the largest percolation cluster of dropped particles with different structures and forms that occupy more than a single site on the lattice. The aggregates are grown on such clusters, in the range the concentration, p$p$, from the percolation threshold, _pc$p_c$ up to the jamming coverage, _pj$p_j$. At the percolation threshold, the aggregates are asymmetrical and the branches are relatively few. However, for larger values of p$p$, the patterns change gradually to a pure DLA. Tiny qualitative differences in this behavior are observed for different k$k$ sizes. Correspondingly, the fractal dimension of the aggregates increases as p$p$ raises in the same range _pc≤p≤_pj$p_c\le p\le p_j$. This behavior is analyzed and discussed in the framework of the existing theoretical approaches.     

Determination of loads applied perpendicularly to the outer boundary of a ring using coefficients of influence

A procedure is explained to determined the amount of several pairs of diametrical loads applied to the outside boundary of a ring when stresses at selected points of the inside or outside boundaries are known. Coefficients of influence are used, following an approach similar to the one presented in a previous paper. Examples of application are given and the possible increase in precision is shown when the number of points of measurements is larger than the number of loads to be determined.     

First-order phase transitions in repulsive rigid k-mers on two-dimensional lattices

In a previous paper [F. Roma?, A. J. Ramirez-Pastor, and J. L. Riccardo, Phys. Rev. B 72, 035444 (2005)], the critical behavior of repulsive rigid rods of length k (k-mers) on a square lattice at half coverage has been studied by using Monte Carlo (MC) simulations. The obtained results indicated that (1) the phase transition occurring in the system is a second-order phase transition for all adsorbate sizes k; and (2) the universality class of the transition changes from 2D Ising-type for monomers (k = 1) to an unknown universality class for k ≥ 2. In the present work, we revisit our previous results together with further numerical evidences, resulting from new extensive MC simulations based on an efficient exchange algorithm and using high-performance computational capabilities. In contrast to our previous conclusions (1) and (2), the new numerical calculations clearly support the occurrence of a first-order phase transition for k ≥ 2. In addition, a similar scenario was found for k-mers adsorbed on the triangular lattice at coverage k/(2k+1).     

Phase diagram of self-assembled rigid rods on two-dimensional lattices: theory and Monte Carlo simulations

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.     

Monte Carlo simulation of metal deposition on foreign substrates

The deposition of a metal on a foreign substrate is studied by means of grand canonical Monte Carlo simulations and a lattice-gas model with pair potential interactions between nearest neighbors. The influence of temperature and surface defects on adsorption isotherms and differential heat of adsorption is considered. The general trends can be explained in terms of the relative interactions between adsorbate atoms and substrate atoms. The systems Ag/Au(1 0 0), Ag/Pt(1 0 0), Au/Ag(1 0 0) and Pt/Ag(1 0 0) are analyzed as examples.     

Ground-State Entropy of ±J Ising Lattices by Monte Carlo Simulations

An accurate numerical calculation of the ground-state entropy associated to two-dimensional ±J Ising lattices is presented. The method is based on the use of the thermodynamic integration method. Total energy is calculated by means of the Monte Carlo method. Then the entropy (or degeneracy) of a state of interest is obtained by using thermodynamic integration starting at a known reference state. Results for small sizes are compared to exact values obtained by exhaustive scanning of the entire ground-state manifold, which serves as a test for the reliability of the simulation model developed here. The close agreement between simulated and exact results for energy and remnant entropy supports the validity of the technique used for describing the properties of ±J Ising lattices at the fundamental level. Finally, the results are extrapolated in order to estimate tendencies for larger systems.     

Percolation of dimers on square lattices

A theoretical approach, based on exact calculations of configurations on finite rectangular cells, is applied to study the percolation of homonuclear dimers on square lattices. An efficient algorithm allows us to calculate the detailed structure of the configuration space for M=_Lx×_Ly$M=L_x\times L_y$ cells, with M$M$ varying from 16 to 36. The percolation process has been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied sites. The percolation threshold has been calculated by means of two complementary methods: one based on well-known renormalization techniques and the other based on determining the inflection point of the percolation function curves. A comparison of the results obtained by these two methods has been performed. The study includes the use of finite-size scaling theory to extrapolate numerical results towards the thermodynamic limit. The effect of jamming due to dimers is also established. Finally, the critical exponents ν$\nu$, β$\beta$ and γ$\gamma$ have been obtained and values compared with numerical results and expected theoretical estimations. The present results show agreement and even improvement (in the case of γ$\gamma$) with respect to some numeric values available in the literature.     

Percolation of polyatomic species with the presence of impurities

In this paper, the percolation of (a) linear segments of size k and (b) k-mers of different structures and forms deposited on a square lattice contaminated with previously adsorbed impurities have been studied. The contaminated or diluted lattice is built by randomly selecting a fraction of the elements of the lattice (either bonds or sites) which are considered forbidden for deposition. Results are obtained by extensive use of finite size scaling theory. Thus, in order to test the universality of the phase transition occurring in the system, the numerical values of the critical exponents were determined. The characteristic parameters of the percolation problem are dependent not only on the form and structure of the k-mers but also on the properties of the lattice where they are deposited. A phase diagram separating a percolating from a nonpercolating region is determined as a function of the parameters of the problem. A comparison between random site and random bond percolation in the presence of impurities on the lattice is presented.