Monte Carlo study of the interfacial adsorption of the Blume-Capel model

TL;DR

This study uses Monte Carlo simulations to analyze the interfacial adsorption scaling in the two-dimensional Blume-Capel model across different transition regimes, including effects of quenched disorder.

Contribution

It provides a detailed numerical verification of scaling behaviors at first- and second-order transitions and near the tricritical point, including the impact of quenched randomness.

Findings

Numerical results confirm expected free-energy scaling scenarios.

Interfacial adsorption exhibits non-divergent scaling with quenched disorder.

Size dependence of adsorption is characterized across transition regimes.

Abstract

We investigate the scaling of the interfacial adsorption of the two-dimensional Blume-Capel model using Monte Carlo simulations. In particular, we study the finite-size scaling behavior of the interfacial adsorption of the pure model at both its first- and second-order transition regimes, as well as at the vicinity of the tricritical point. Our analysis benefits from the currently existing quite accurate estimates of the relevant (tri)critical-point locations. In all studied cases, the numerical results verify to a level of high accuracy the expected scenarios derived from analytic free-energy scaling arguments. We also investigate the size dependence of the interfacial adsorption under the presence of quenched bond randomness at the originally first-order transition regime (disorder-induced continuous transition) and the relevant self-averaging properties of the system. For this ex-first-order regime, where strong transient effects are shown to be present, our findings support the scenario of a non-divergent scaling, similar to that found in the original second-order transition regime of the pure model.