Non-Arrhenius Behavior of Surface Diffusion near a Phase Transition Boundary

We study the non-Arrhenius behavior of surface diffusion near the second-order phase transition boundary of an adsorbate layer. In contrast to expectations based on macroscopic thermodynamic effects, we show that this behavior can be related to the average microscopic jump rate, which in turn is determined by the waiting-time distribution $W\left(t\right)$ of single-particle jumps at short times. At long times, $W\left(t\right)$ yields a barrier that corresponds to the rate-limiting step in diffusion. The microscopic information in $W\left(t\right)$ should be accessible by scanning tunneling microscopy measurements.