A transfer matrix approach is used to conduct a thorough investigation of all possible adsorbate configurations or phases on terraces of various widths M including edge effects, and limited to first- and second-neighbor adsorbate-adsorbate interactions. Figures showing the configurations that occur within this model are presented for M = 3 and 4, and detailed tables provide the phase sequences corresponding to all possible ranges of values for the interaction energies. Higher width terrace results have also been completed and are available upon request. As such, the model calculations provide a useful reference for experimentalists leading to predictions of the values of the interaction energies from the observed phase sequence and the conditions prevailing at the transition between phases. A few experimental results are interpreted using the model. One suggests specific experiments, which would make the observations more amenable to direct comparison with the calculations. (C) 2003 Elsevier Science B.V. All rights reserved.