https://doi.org/10.1007/s100530070027
Adatom diffusion on a square lattice. Theoretical and numerical studies
1
Institute of Physics, National Academy of Sciences of Ukraine Prospect Nauki 46, 252028, Kyiv 28, Ukraine
2
Departamento de Física and Centro Latinoamericano de Estudios Ilya Prigogine, Universidad Nacional de
San Luis,
CONICET, Chacabuco 917, 5700 San Luis, Argentina
3
Institute of Physics, Academy of Sciences of the Czech Republic Na Slovance 2, 180 40 Praha 8, Czech
Republic
4
Max-Planck-Institut für Eisenforschung, Max-Planck Strasse 1, 40074 Düsseldorf, Germany
5
Lehrstuhl für Physikalische Chemie II, Universität Dortmund, 44227 Dortmund, Germany
Received:
1
September
1998
Revised:
8
March
2000
Published online: 15 November 2000
A two-dimensional lattice-gas model with square symmetry is
investigated by using the real-space renormalization group (RSRG) approach
with blocks of different size and symmetries. It has been shown
that the precision of the method depends strongly not only on the number of
sites in the block but also on its symmetry. In general, the
accuracy of the method increases with the number of sites in the block.
The minimal relative error in determining the critical values of
the interaction parameters is equal to 
.
Using the RSRG method, we have explored phase diagrams of both a
two-dimensional Ising spin model and of a square lattice gas with lateral
interactions between adparticles. We also have investigated the influence of
the attractive and repulsive interactions on both the thermodynamic
properties of the lattice gas and the diffusion of adsorbed particles over
surface. We have calculated adsorption isotherms and coverage dependences of
the pair correlation function, isothermal susceptibility and the chemical
diffusion coefficient. In addition, we have included in our analysis the
interaction of the activated particle in the saddle point with its nearest
neighbors. We have also used Monte Carlo (MC) technique to calculate these
dependences. Despite the fact that both methods constitute very different
approaches, the correspondence of the numerical data is surprisingly good.
Therefore, we conclude that the RSRG approach can be applied to
characterize the thermodynamic and kinetic properties of systems of
particles with strong lateral interactions.
PACS: 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 68.35.Rh – Phase transitions and critical phenomena / 68.35.Fx – Diffusion; interface formation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
