Surface diffusion near first-order phase transitions for a model on a triangular lattice

Abstract

We rigorously study the thermodynamic factor of surface diffusion for a two-dimensional one-component lattice-gas system on a regular triangular lattice. First, we prove that four low-temperature phases exist in the system, their surface coverages being 0, 1/3, 2/3 and 1, and that, depending on the interparticle interactions, a phase transition between any two of them can occur. Three of these transitions are shown to be of first order at low temperatures, while in the other three cases there is an infinite number of ground states, yielding in fact a residual entropy. Then, for the three first-order phase transitions, we provide explicit finite-size formulae for the free energy, surface coverage and isothermal susceptibility, showing their low-temperature dependence on the chemical potential and the total number of adsorption sites. Using these formulae, we numerically obtain the coverage dependence of the thermodynamic factor and compare it with analytical results.

Modelling of phase transitions: do it yourself

“…Here we shall use model (1) to show how its equilibrium behaviour at low temperatures can be studied. Our main focus will be on the structure of the model phases and the possible occurrence of phase transitions (these results were originally obtained in [12]). First, we describe the application of the technique to a general lattice model, splitting it into four steps, and then to model (1).…”