A two-dimensional lattice-gas model of square symmetry was investigated by using the real-space renormalization group approach with blocks of different size and symmetry. It was shown that the precision of the method depended strongly not only upon the number of sites in the block but also on its symmetry. In general, the accuracy of the method increased with the number of sites in the block. The most accurate results were obtained for the largest cluster, containing 34 sites. The minimal relative error in determining the critical values of interaction parameter was 0.13%. It was shown that the "antiferromagnetic majority rule" for the choice values of block spins gave much better results for the repulsion between the adsorbed particles, as compared to the ordinary "majority rule." Using the real-space renormalization group method, phase diagrams of a two-dimensional Ising spin model and of a square lattice gas with lateral interactions between ad-particles were explored. Adsorption isotherms for various temperatures, the coverage and temperature dependences of the pair correlation function for the nearest-neighbor ad-particles and the chemical diffusion coefficient, the temperature dependence of the specific heat and the coverage dependences of the isothermal susceptibility for various temperatures were all calculated. These quantities had also been obtained by Monte Carlo simulation. Despite the fact that the methods involved very different approaches, the correspondence of the numerical data was surprisingly good. It was therefore concluded that the real-space renormalization group method could be applied, at least for the present systems, to characterization of the thermodynamic and kinetic properties of interacting adsorbates.

Adatom Diffusion on a Square Lattice: Comparison of Real-Space Renormalization Group and Monte Carlo Approaches. A.A.Tarasenko, L.Jastrabík, F.Nieto, C.Uebing: Physical Review B, 1999, 59[12], 8252-61