arXiv subjects
Publications and source records attributed to Felix Nieto.
Some results about the geodesic boundary of minimal surfaces in $\mathbb{H}^2\times \mathbb{R}$ are generalized for surfaces of constant mean curvature surfaces $H$, with $0\le H\le 1/2$.
In the present paper, the connection between surface order-disorder phase transitions and the percolating properties of the adsorbed phase has been studied. For this purpose, four lattice-gas models in presence of repulsive interactions have been considered. Namely, monomers on honeycomb, square and triangular lattices, and dimers (particles occupying two adjacent adsorption sites) on square substrates. By using Monte Carlo simulation and finite-size scaling analysis, we obtain the percolation threshold $θ_c$ of the adlayer, which presents an interesting dependence with $w/k_BT$ (being $w$, $k_B$ and $T$, the lateral interaction energy, the Boltzmann's constant and temperature, respectively). For each geometry and adsorbate size, a phase diagram separating a percolating and a non-percolating region is determined.
In this paper the percolation of monomers on a square lattice is studied as the particles interact with either repulsive or attractive energies. By means of a finite-size scaling analysis, the critical exponents and the scaling collapsing of the fraction of percolating lattice are found. A phase diagram separating a percolating from a non-percolating region is determined. The main features of the phase diagram are discussed in terms of simple considerations related to the interactions present in the problem. The influence of the phase transitions occurring in the system is reflected by the phase diagram. In addition, a scaling treatment maintaining constant the surface coverage and varying the temperature of the system is performed. In all the considered cases, the universality class of the model is found to be the same as for the random percolation model.