  The coverage of vicinal, stepped surfaces with molecules is simulated with
the help of a two-dimensional Ising model including local distortions and an
Ehrlich-Schwoebel barrier term at the steps. An effective two-spin model is
capable to describe the main properties of this distorted Ising model. It is
employed to analyze the behavior of the system close to the critical points.
Within a well-defined regime of bonding strengths and Ehrlich-Schwoebel
barriers we find a reduction of coverage (magnetization) at low temperatures
due to the presence of the surface step. This results in a second,
low-temperature transition besides the standard Ising order-disorder
transition. The additional transition is characterized by a divergence of the
susceptibility as a finite-size effect. Due to the surface step the mean-field
specific heat diverges with a power law.
