Equilibrium island-size distribution in one dimension revisited: analytical models and Monte Carlo simulations

Abstract

The island size distribution, at thermodynamic equilibrium, of interacting particles in a one-dimensional lattice-gas model is revisited. A derivation for the exact island size distribution of nearest neighbor interacting particles using the detailed balance principle is proposed and it is shown that it agrees with the distribution obtained by Gambardella et al who resorted to the minimization of the free energy (2006 Phys. Rev. B 73 245425). We find that the island size distributions change from an exponential shape to one exhibiting a maximum when repulsive interactions with distant neighbors are considered. In this work we present an analytical model that successfully reproduces the island size distribution obtained from Monte Carlo simulations for both interaction schemes and any coverage.