SOLVATION FORCE IN 2-DIMENSIONAL ISING STRIPS

Finite-size contributions to the free energy of a fluid confined between two parallel walls, separated by a distance L, give rise to an excess pressure which is termed the solvation force f(solv)(L). Using exact transfer-matrix methods we calculate the analog of f(solv) for a two-dimensional Ising strip of infinite length and finite width L = na, where n is the number of layers and a is the lattice spacing, for bulk field h = 0 and fixed (+/+) and (+/-) boundary conditions on the spins in the surface layers. + and - refer to up and down spins, respectively. f(solv)(++) is negative (attractive force) for all temperatures T and for a given L has its minimum above the critical temperature T(c). The amplitude of the force at the minimum is about 6.6 times the value at T(c), the ''Casimir'' amplitude. In the (+/-) strip a + - interface develops at all subcritical temperatures and entropic repulsion gives rise to a positive f(solv)(+-) which has its maximum slightly below T(c). Universal scaling forms are derived for both cases and accurate approximations, valid for low, near critical, and high temperatures, are obtained. In the scaling limit, L --> infinity, t[=(T-T(cv))/T(c)]-->0, the minimum of f(solv)(++) is given by nt(min) = 2642 and the maximum of f(solv)(+-) by nt(max) = -0.2735. We compare and contrast our results with earlier predictions based on mean-field analyses and scaling arguments.