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 cells,...

Percolation due to the simultaneous occupation of two neighboring bond sites, namely a bond dimer, is considered here by means of the renormalization cell technique providing an analytic way to obtain results such as percolation threshold, jamming coverage and critical exponents. This is...

In this paper, the percolation of mixtures of monomers and polyatomic species (k-mers) on a square lattice is studied. By means of a finite-size scaling analysis, the critical exponents and the scaling collapsing of the fraction of percolating lattices are found. A phase diagram separating a...

We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards–Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two- and three-dimensional lattices. By a systematic analysis we find a simple formula to...

The site percolation problem on square lattices whose sites are grouped in two types of energetically different patches is studied. Several lattices formed by collections of either randomly or orderly localized and no overlapped patches of different sizes are generated. The system is...

A novel order parameter Φ for spin glasses is defined based on topological criteria and with a clear physical interpretation. Φ is first investigated for well known magnetic systems and then applied to the Edwards–Anderson ±J model on a square lattice, comparing its properties with the...

The Edwards–Anderson site order parameter, q, or its generalizations have been considered to study the partial spin-glass behavior of ±J Ising lattices. These parameters vanish if all 2W ground states are taken into account, so an ergodic separation must be done in order to emulate nature....

The percolation problem of interacting particles on square lattices with two kinds of energetically different sites is studied. Square lattices formed by collections of either randomly or orderly distributed sites are generated. The system is characterized by two parameters, namely, the...

Square lattices with Ising spins at the sites and ±J exchange interactions between nearest neighbors are one of the realizations of the Edwards–Anderson model originally proposed to mimic spin glasses. Such systems produce a complex configuration space due to frustration originated in local...

Grand canonical Monte Carlo simulations have been performed in order to study adsorption thermodynamics of pairwise interacting particles on fractal surfaces. Diffusion-limited aggregates (DLA) have been used as a substrate where interacting particles are adsorbed. In order to obtain aggregates...