  The self-assembly of submonolayer amounts of Au on the densely stepped
Si(553) surface creates an array of closely spaced \atomic wires" separated by
1.5 nm. At low temperature, charge transfer between the terraces and the row of
silicon dangling bonds at the step edges leads to a charge-ordered state within
the row of dangling bonds with x3 periodicity. Interactions between the
dangling bonds lead to their ordering into a fully two-dimensional (2D) array
with centered registry between adjacent steps. We show that as the temperature
is raised, soliton defects are created within each step edge. The concentration
of solitons rises with increasing temperature and eventually destroys the 2D
order by decoupling the step edges, reducing the effective dimensionality of
the system to 1D. This crossover from higher to lower dimensionality is
unexpected and, indeed, opposite to the behavior in other systems.
