The wetting transition of the Blume-Capel model is studied by a finite-size scaling analysis of $L\times M$ lattices where competing boundary fields $\pm H_1$ 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 $\alpha =-1$, $\beta =0$, and $\gamma =3$. These concepts are also verified for the Ising model. For the Blume-Capel model, it is found that the field strength $H_{1c}\left(T\right)$ where critical wetting occurs goes to zero when the bulk second-order transition is approached, while $H_{1c}\left(T\right)$ 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.

• Received 27 January 2012

DOI:https://doi.org/10.1103/PhysRevE.85.061601