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 th e form H(n) = +/-h[n(-3) - (L - n + 1)(-3)], where n = 1, 2,..., L labels t he rows across the strip. In the case of competing fields and L --> infinit y, the system exhibits a critical wetting transition of a similar type as i n the well studied case of short-range boundary fields. At finite L, this w etting transition is replaced by a (rounded) interface localization-delocal ization transition at T-c(h, L). The order parameter profiles and correlati on function G(parallel to)(n, r), where r is a coordinate parallel to the b oundaries of the strip, are analysed in detail. It is argued that for T gre ater 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 p roportional 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 c ase. In addition to this case of competing boundary fields, also the case w here both boundaries are sources of fields of the same sign is studied, whi ch then compete with a uniform bulk field such that a capillary condensatio n transition occurs. The data obtained are consistent with the Kelvin equat ion as in the case of the short-range surface fields.