Wall effects in critical systems: Scaling in Ising model strips

A scaling theory and a related conjecture presented recently by de Gennes and Fisher to predict the effects of walls inserted in two near-critical binary fluid mixtures, are checked theoretically by exact analytic calculations for n×∞, two-dimensional Ising model strips with a surface field, h₁, imposed on the first layer; exact calculations with a second surface field, hₙ, imposed on the nth layer are also reported. It is verified, in particular, that the effects on properties observed close to one wall of a second wall at distance D decay, at the critical point, as 1Dᵈ, where d is the spatial dimensionality. In addition to the scaling limits, the leading corrections are calculated explicitly and presented graphically.