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(t) of single-particle jumps at
short times. At long times, W(t) yields a barrier that corresponds to the
rate-limiting step in diffusion. The microscopic information in W(t) should be
accessible by STM measurements.Comment: 4 pages, Latex with RevTeX macro