Interfacial adsorption in two-dimensional Potts models

TL;DR

This paper investigates interfacial adsorption in two-dimensional q-state Potts models at first-order transitions, using simulations and analytical methods to understand its behavior near the critical temperature.

Contribution

It combines Monte Carlo and density-matrix renormalization group methods to confirm and extend analytic predictions of interfacial adsorption scaling in Potts models.

Findings

W  t^{-1/3} scaling near T_c

Numerical estimates of corrections to scaling

Support for previous low-temperature expansion results

Abstract

The interfacial adsorption W at the first-order transition in two-dimensional q-state Potts models is studied. In particular, findings of Monte Carlo simulations and of density-matrix renormalization group calculations, at q= 16, are consistent with the analytic result, obtained in the Hamiltonian limit at large values of q, that W \propto t^{-1/3} on approach to the bulk critical temperature T_c, t=|T_c-T|/T_c. In addition, the numerical findings allow to estimate corrections to scaling. Our study supports and specifies a previous conclusion by Bricmont and Lebowitz based on low-temperature expansions.