Wetting in a two-dimensional random-bond Ising model

We analyze a square-lattice random-bond Ising model using a numerical transfer-matrix technique to test the theory proposed by Lipowsky and Fisher for the complete wetting transition of a wall by one of two phases which coexist in a random medium. The theoretical scaling arguments are checked in detail. The transverse and longitudinal correlation lengths, ξ_⊥(h) and ξ_∥(h), are found to be related by ξ_⊥{~}ξ_∥^ζ with {ζ}=0.65±{}0.02 as the external field, or chemical potential deviation, h, approaches 0: the theoretical expectation is {ζ}=(2/3. The mean wetting layer thickness diverges as l{}(h){~}h^-ψ while as h{→}0 with {ψ}=ν_⊥=(1/2. .AE