Kontron (Germany)

Critical, tricritical, and first-order wetting transitions are studied near the bulk critical point of a simple cubic nearest-neighbor Ising model by extensive Monte Carlo simulations. The model applies an exchange J in the bulk and exchange ${J}_{s}$ in the surface planes, where surface fields ${H}_{1}$ also act in addition to a possible bulk field H. Lattices in a thin-film geometry L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}D are used, with two free L\ifmmode\times\else\texttimes\fi{}L surfaces (with L up to 256) and film thickness D up to 160, applying a very fast fully vectorizing multispin coding program. Our results present the first quantitative evidence for the scaling theory due to Nakanishi and Fisher, which links wetting behavior and surface critical behavior. In particular, we show that the tricritical wetting line (${J}_{s}^{t}$/J) merges into the surface-bulk multicritical point with associated critical field ${H}_{1t}$\ensuremath{\sim}(1-T/${T}_{c}$${)}^{\ensuremath{\Delta}1m}$, while the critical field for critical wetting ${H}_{1c}$ vanishes as , where ${\ensuremath{\Delta}}_{1}$(${\ensuremath{\Delta}}_{1m}$) are the ``gap'' exponents for the surface-layer magnetization at the ordinary (or surface-bulk multicritical) transition. The mean-field character of critical wetting in this model is again confirmed.

It is the aim of this chapter to enable the readers to implement solutions to problems in the physical sciences with a computer program, and carry out the ensuing computer studies. They will therefore be shown a few basic numerical methods, and the general spirit for mapping physics problems onto a computational algorithm. It is advisable to spend some time actually implementing the exercises proposed, since is only by so doing that one may learn about, and get a feel for, the spirit of scientific computing. Examples are given using the FORTRAN 77 language and the UNIX operating system. The graphics interface used is that of the SUN workstation.