Exact results for the solvation force in 2D Ising stripes

The solvation force for two-dimensional Ising stripes in the presence of boundary fields is calculated via exact diagonalization of the transfer matrix in two cases: the symmetric case corresponds to identical boundary fields and the antisymmetric case to exactly opposite boundary fields. In the symmetric case the solvation force is always negative (attractive), while in the antisymmetric case it is positive (repulsive) at high temperatures and negative at low temperatures. It changes sign close to the critical wetting temperature characterizing the semi-infinite system. The properties of the solvation force are discussed, and the scaling function describing its dependence on temperature, boundary field, and stripe's width is proposed.