Monte Carlo simulations of the 2d-Ising model in the geometry of a long stripe

Abstract

The two-dimensional Ising model in the geometry of a long stripe can be regarded as a model system for the study of nanopores. As a quasi-one-dimensional system, it also exhibits a rather interesting “phase behavior”: At low temperatures the stripe is either filled with “liquid” or “gas” and “densities” are similar to those in the bulk. When we approach a “pseudo-critical point” (below the critical point of the bulk) at which the correlation length becomes comparable to the length of the stripe, several interfaces emerge and the systems contains multiple “liquid” and “gas” domains. The transition depends on the size of the stripe and occurs at lower temperatures for larger stripes. Our results are corroborated by simulations of the three-dimensional Asakura–Oosawa model in cylindrical geometry, which displays qualitatively similar behavior. Thus our simulations explain the physical basis for the occurrence of “hysteresis critical points” in corresponding experiments.