Wetting Transition in the Two-Dimensional Blume-Capel Model: A Monte Carlo study

TL;DR

This study investigates the wetting transition in the two-dimensional Blume-Capel model using Monte Carlo simulations, revealing critical behavior and phase diagram features near the tricritical point.

Contribution

It provides a finite-size scaling analysis of wetting transitions in the 2D Blume-Capel model, establishing equivalence with bulk critical phenomena and exploring phase behavior near the tricritical point.

Findings

Critical wetting in 2D is equivalent to a bulk critical phenomenon with specific exponents.

The critical field strength for wetting vanishes near the second-order transition but remains finite near the first-order transition.

Interfaces exhibit phase enrichment and finite thickness in the second-order case.

Abstract

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 row 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 $H_{1c} (T)$ where critical wetting occurs goes to zero when the bulk second-order transition is approached, while $H_{1c}(T)$ 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 also is given.