DIFFUSION ON A HONEYCOMB LATTICE - REAL-SPACE RENORMALIZATION-GROUP APPROACH

A two-dimensional lattice-gas model with honeycomb symmetry is investi gated by using the real-space renormalization group (RSRG) approach wi th a number of RSRG transformations based on clusters of different sym metries and sizes (up to 42 sites). The accuracy of calculations is fo und to be a nonmonotonic function of the size of a cluster, and to dep end strongly on its symmetry. The highest obtained accuracy with respe ct to the determination of the critical value of the pair interaction parameter is 0.38%. The phase diagram of the Ising antiferromagnetic s pin model and of the corresponding lattice-gas model is constructed wi th this accuracy. The ordered phase in the lattice system is shown to appear in the very narrow density interval, 0.447 <n<0.553. In additio n, the coverage dependence of the chemical diffusion coefficient and m ean-square density fluctuations are studied at temperatures below the critical one. Both quantities are demonstrated to exhibit singularitie s at the critical coverages. The type of singularities tin particular, the critical slowdown of diffusion) is in agreement with the predicti ons of the scaling theory and also with recent results obtained for a model treating the effect of surface reconstruction on diffusion.