Wetting transition in the two-dimensional Blume-Capel model: A Monte Carlo study

Abstract

The wetting transition of the Blume-Capel model is studied by a finite-size scaling analysis of L × M lattices where competing boundary fields ±H1 act on the first or last row of the L rows in the strip, respectively. We show that using the appropriate anisotropic version of finite-size scaling, critical wetting in d = 2 is equivalent to a “bulk” critical phenomenon with exponents α = −1, β = 0, and γ = 3. These concepts are also verified for the Ising model. For the Blume-Capel model, it is found that the field strength H1c(T ) where critical wetting occurs goes to zero when the bulk second-order transition is approached, while H1c(T ) stays nonzero in the region where in the bulk a first-order transition from the ordered phase, with nonzero spontaneous magnetization, to the disordered phase occurs. Interfaces between coexisting phases then show interfacial enrichment of a layer of the disordered phase which exhibits in the second-order case a finite thickness only. A tentative discussion of the scaling behavior of the wetting phase diagram near the tricritical point is also given.