  We report results of a theoretical study on an adsorbate induced surface
reconstruction. Hydrogen adsorption on a W(100) surface causes a switching
transition in the symmetry of the displacements of the W atoms within the
ordered c(2x2) phase. This transition is modeled by an effective Hamiltonian,
where the hydrogen degrees of freedom are integrated out. Based on extensive
Monte Carlo renormalisation group calculations we show that the switching
transition is of second order at high temperatures and of first order at low
temperatures. This behavior is qualitatively explained in terms of an XY model
where there is an interplay between four and eight fold anisotropy fields. We
also compare the calculated phase diagrams with a simple mean field theory.
