Collective surface diffusion near a first-order phase transition
  For a large class of lattice models we study the thermodynamic factor, $\Phi$, of the collective surface diffusion coefficient near a first-order phase transition between two phases at low temperatures. In a two-phase regime its dependence on the coverage, $\te$, is $\Phi \approx \te/[(\te-\te_-)(\te_+ - \te)N]$, where $N$ is the number of adsorption sites and $\te_\pm$ are the single-phase coverages at the transition. In the crossover between the two-phase and single-phase regimes $\Phi(\te)$ is shown to have a more complex behavior. The results are applied to a simple 2D lattice model. 
Igor Medved' and Anton Trn\'ik
cond-mat.stat-mech