The Ising model as a playground for the study of wetting and interface behavior

Computer simulations have played an important role in the elucidation of wetting and interface unbinding phenomena. In particular, use of the Ising-lattice-gas model in a film geometry and subject to diverse surface and bulk magnetic fields has permitted extensive Monte Carlo simulations to reveal new features of the phase diagrams associated with these phenomena and to provoke new theoretical studies. The status of our knowledge about the nature of wetting and interface-delocalization transitions which has resulted from these Ising model simulations will be summarized.

Wetting in fluid systems. Wetting and capillary condensation of lattice gases in thin film geometry

Monte Carlo studies of lattice gas models with attractive interactions between nearest neighbors on a simple cubic lattice are carried out for a L×L×D geometry with two hard walls of size L×L and periodic boundary conditions parallel to the wall. Two types of short-range forces at the walls are considered: (i) Both walls are of the same type and exert an attractive force of the same strength (in Ising model terminology, surface fields HD = H1 occur). (ii) The walls differ, one attracts and the other repels particles, again with the same strength (HD = −H1). In the first case, capillary condensation occurs at a chemical potential differing from its value for phase coexistence in the bulk, an…

Statistical and systematic errors in Monte Carlo sampling

We have studied the statistical and systematic errors which arise in Monte Carlo simulations and how the magnitude of these errors depends on the size of the system being examined when a fixed amount of computer time is used. We find that, depending on the degree of self-averaging exhibited by the quantities measured, the statistical errors can increase, decrease, or stay the same as the system size is increased. The systematic underestimation of response functions due to the finite number of measurements made is also studied. We develop a scaling formalism to describe the size dependence of these errors, as well as their dependence on the “bin length” (size of the statistical sample), both…

Thin Ising films with competing walls: A Monte Carlo study.

Ising magnets with a nearest neighbor ferromagnetic exchange interaction J on a simple cubic lattice are studied in a thin film geometry using extensive Monte Carlo simulations. The system has two large L\ifmmode\times\else\texttimes\fi{}L parallel free surfaces, a distance D apart from each other, at which competing surface fields act, i.e., ${\mathit{H}}_{\mathit{D}}$=-${\mathit{H}}_{1}$. In this geometry, the phase transition occurring in the bulk at a temperature ${\mathit{T}}_{\mathit{c}\mathit{b}}$ is suppressed, and instead one observes the gradual formation of an interface between coexisting phases stabilized by the surface fields. While this interface is located in the center of th…

Considerations on correlations in shift-register pseudorandom number generators and their removal

Abstract We present a simple calculation quantitatively explaining the triplet correlations in the popular shift-register random number generator “R250”, which were recently observed numerically by Schmid and Wilding, and are known from general analysis of this type of generator. Starting from these considerations, we discuss various methods to remove these correlations by combining different shift-register generators. We implement and test a particularly simple and fast version, based on an XOR combination of two independent shift-register generators with different time lags. The results indicate that this generator has much better statistical properties than R250, while being only a facto…

Character of the Phase Transition in Thin Ising Films with Competing Walls

By extensive Monte Carlo simulations of a lattice gas model we have studied the controversial nature of the gas-liquid transition of a fluid confined between two parallel plates that exert competing surface fields. We find that the transition is shifted to a temperature just below the wetting transition of a semi-infinite fluid but belongs to the two-dimensional Ising universality class. In between this new type of critical point and bulk criticality, a response function ${x}_{\mathrm{nn}}^{max}$ varying exponentially with $D$ is observed, $\frac{2 \mathrm{ln}{\ensuremath{\chi}}_{\mathrm{nn}}^{max}}{D}={\ensuremath{\ell}}^{\ensuremath{-}1}$, where $\ensuremath{\ell}$ is a new length charact…

Interface localization transition in Ising films with competing walls: Ginzburg criterion and crossover scaling.