Surface order-disorder phase transitions and percolation

TL;DR

This study explores how surface order-disorder phase transitions relate to percolation properties in lattice-gas models with repulsive interactions, using Monte Carlo simulations to identify percolation thresholds and phase diagrams.

Contribution

It provides a detailed analysis of percolation thresholds in various lattice-gas models, linking phase transitions to percolation behavior with finite-size scaling.

Findings

Percolation threshold $ heta_c$ depends on $w/k_BT$ for different lattices and adsorbates.

Phase diagrams delineate percolating and non-percolating regions.

Monte Carlo simulations effectively determine percolation properties in surface adsorption models.

Abstract

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 $\theta_c$ 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.