Finite-size scaling behavior of the tracer surface diffusion coefficient near a second-order phase transition

We investigate the finite-size scaling behavior 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 measured tracer surface diffusion coefficient, Dt, is a smooth function, having an inflexion point at critical temperature. Its derivative, $\partial D_{\rm t}/\partial(1/k_{\rm B}T)$, exhibits cusp-like maximum which is a) sharply pronounced and b) converged to $T_{\rm c}(\infty)$ for large lattice sizes. We have analyzed the finite-size behavior of Dt and obtained its critical exponent $\sigma_{\rm t}=0.665\pm0.003$