6533b831fe1ef96bd12983be

RESEARCH PRODUCT

The Ising square lattice in aL�M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers

subject

description

Critical phenomena in adsorbed monolayers on surfaces are influenced by limited substrate homogeneity, such as surface steps. We consider the resulting finite-size and boundary effects in the framework of a lattice gas system with nearest neighbor attraction in aL×M geometry, with two free boundaries of lengthM≫L, and periodic boundary conditions in the other direction (along the direction of the steps). This geometry thus models a “terrace” of the stepped surface, and adatoms adsorbed on neighboring terraces are assumed to be non-interacting. Also the effect of boundary “fields” is considered (describing the effects of missing neighbors and changed binding energy to the substrate near the boundary). Extensive Monte Carlo calculations on this model performed on a multi-transputer system are presented and analyzed in terms of phenomenological finite size scaling concepts. The fact that two scaling variables occur (ζ/L,L/M, with ζ being the correlation length in the bulk) is demonstrated explicitly. In the absence of boundary fields, the system forM≫L orders nearTc in a domain state, with domain walls running across the terrace, while at some temperature belowTc a transition to a monodomain state occurs. This domain state slightly belowTc is suppressed, however, by rather weak boundary fields. These results are interpreted in terms of exact theoretical predictions.