Interfacial adsorption in two-dimensional pure and random-bond Potts models

TL;DR

This study uses Monte Carlo simulations to analyze interfacial adsorption in two-dimensional Potts models, revealing scaling behaviors at various phase transitions for pure and disordered systems.

Contribution

It provides new insights into the finite-size scaling of interfacial adsorption in both pure and random-bond two-dimensional Potts models across different phase transition types.

Findings

Supports early scaling predictions for pure systems.

Discusses interfacial adsorption at continuous transitions in disordered systems.

Analyzes self-averaging properties and size extrapolation of interfacial adsorption.

Abstract

We study using Monte Carlo simulations the finite-size scaling behavior of the interfacial adsorption of the two-dimensional square-lattice $q$-states Potts model. We consider the pure and random-bond versions of the Potts model for $q = 3,4,5,8$ and $q = 10$, thus probing the interfacial properties at the originally continuous, weak, and strong first-order phase transitions. For the pure systems our results support the early scaling predictions for the size dependence of the interfacial adsorption at both first- and second-order phase transitions. For the disordered systems, the interfacial adsorption at the (disordered induced) continuous transitions is discussed, applying standard scaling arguments and invoking findings for bulk critical properties. The self-averaging properties of the interfacial adsorption are also analyzed by studying the infinite limit-size extrapolation of properly defined signal-to-noise ratios.