Ising systems with pairwise competing surface fields

Abstract

The magnetization distribution and phase behaviour of large but finite Ising simple cubicL × L × L lattices ind = 3 dimensionsand square L × L lattices in d = 2 dimensions are studied for the case where four free boundaries are present, at which surface fields+Hs act on one pair of opposite boundaries while surface fields−Hs act on theother pair (in d = 3, periodic boundary conditions are used for the remaining pair). Both the distributionPL(m) of the global magnetization and also the distribution of the local magnetizationm(x,z) are obtained by Monte Carlo simulations, wherex and z denote the coordinates when the boundaries are oriented along thex-axis andz-axis(in d = 2); oralong the xy-plane and zy-plane (in d = 3, where the periodic boundary condition applies in they-direction). Varyingthe temperature T and linear dimension L it is found that a single bulk rounded phase transition occurs, which converges to the bulk transitiontemperature Tcb as , unlike other geometric arrangements of competing boundary fields, where a secondtransition occurs in the bulk due to interface formation or delocalization, related to wedgeor corner filling or wetting transitions, respectively. In the present geometry, onlyprecursors of wetting layers form on those boundaries where the field is oppositely orientedto the magnetization in the bulk and the thickness of these layers is found to scale likeL1/2 (in d = 2) or lnL (in d = 3), respectively. These findings are explained in terms of a phenomenological theory basedon the effective interface Hamiltonian and scaling considerations.