Atomic sulfur chemisorbed on Ru(0001) forms a striped network of domain walls (DW's) at coverages above completion of a commensurate (3 × 3) R30°structure (θ>0.333). At high coverages (θ=0.48), this DW network transforms into a homogeneous commensurate c(2×4) structure with an ideal coverage θ=0.50. The temperature-induced phase transitions of the domain walls and the c(2×4) structures were investigated to low-energy electron diffraction spot profile analysis and compared to theoretical predictions. The phase transition of the superheavy walls, formed a low wall concentrations (coverages θ between 0.35 and 0.43), to the disordered lattice gas is found to be continuous, and compatible with a Kosterlitz-Thouless transition expected from theory. At higher coverages light DW's are formed (0.43<θ<0.48), which undergo a first-order transition, as evident from an intervening two-phase region formed by the DW phase and the incommensurate phase. Short-range order correlations are maintained in the disordered phase, which is best described by an incommensurate phase with strong disorder. Again a first-order transition is found for the commensurate c(2×4) structure, which also disorders into a short-range ordered incommensurate phase. Influences by finite-size effects are clearly visible. © 1995 The American Physical Society.