The interactions of ad-atoms on a surface may be modeled with the Ising Hamiltonian conveniently extended to accomodate couplings beyond the simplest nearest neighbor. We use real space renormalization group methods to study the phase diagram for such a model for hydrogen on Pd(100). Confirming the previous Monte Carlo results we find qualitative agreement with experiment at high temperatures but with a too narrow ordered region. We report also the finding of a second order transition to a (2×2) superlattice structure at lower temperatures. {\textcopyright} 1982.