Interfacial adsorption in Potts models on the square lattice

TL;DR

This paper investigates interfacial phenomena in 2D Potts models, analyzing critical behavior and the impact of randomness using Monte Carlo simulations, revealing linear growth of interfacial adsorption profiles with system size.

Contribution

It provides a detailed analysis of interfacial adsorption and critical behavior in both perfect and disordered 2D Potts models, including corrections to scaling and the role of randomness.

Findings

Interfacial adsorption profiles grow linearly with lattice size at criticality.

Randomness influences the interfacial behavior and critical properties.

Scaling arguments help interpret the interfacial phenomena observed.

Abstract

We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) $q$-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, the critical behavior, including corrections to scaling, are analyzed. The role of randomness is scrutinized. Results are discussed applying scaling arguments and invoking findings for bulk critical properties. In all studied cases, i.e., $q = 3$, $4$, and $q = 8$, the spread of the interfacial adsorption profiles is observed to increase linearly with the lattice size at the bulk transition point.