Finite size dependence of the tracer surface diffusion coefficient near a second order phase transition

We investigate the finite size dependences of the tracer surface diffusion coefficient in the vicinity of a second order phase transition. For this purpose, we use a lattice gas model of repulsively interacting particles on a square lattice. For all lattice sizes L studied, the tracer diffusion coefficient, D-t, is a smooth function of temperature. There are no anomalies in the direct temperature dependence of D-t near the critical temperature T-c. However, its derivative, dD(t)/d(1/k(B)T), exhibits cusp-like anomalies which are largely pronounced for large lattice sizes.