Monte Carlo studies of d=2 Ising strips with long-range boundary fields

A two-dimensional Ising model with nearest-neighbour ferromagnetic exchange confined in a strip of width L between two parallel boundaries is studied by Monte Carlo simulations. 'Free' boundaries are considered with unchanged exchange interactions at the boundary but long-range boundary fields of the form H(n) = +/-h[n(-3) - (L - n + 1)(-3)], where n = 1, 2,..., L labels the rows across the strip. In the case of competing fields and L --> infinity, the system exhibits a critical wetting transition of a similar type as in the well studied case of short-range boundary fields. At finite L, this wetting transition is replaced by a (rounded) interface localization-delocalization transition at T-c(h, L). The order parameter profiles and correlation function G(parallel to)(n, r), where r is a coordinate parallel to the boundaries of the strip, are analysed in detail. It is argued that for T greater than or equal to T-c(h, L) the order parameter profile is essentially a linear variation across the strip, i.e. the width omega varies as omega proportional to L. unlike the case in d = 3 where omega proportional to L-1/2 is the shea-range case and omega proportional to ln L in the case of the n(-3) boundary potential holds. The parallel correlation length xi(parallel to) scales as xi(parallel to) proportional to L-2 as for the short-range case. In addition to this case of competing boundary fields, also the case where both boundaries are sources of fields of the same sign is studied, which then compete with a uniform bulk field such that a capillary condensation transition occurs. The data obtained are consistent with the Kelvin equation as in the case of the short-range surface fields.