Analog of surface preroughening in a two-dimensional lattice Coulomb gas

TL;DR

This paper maps a surface roughening and preroughening transition onto a two-dimensional Coulomb gas model, revealing phase behaviors and dielectric properties through simulations and exact calculations.

Contribution

It provides an exact mapping of surface preroughening onto a Coulomb gas model, analyzing phase transitions and dielectric behavior with new theoretical insights.

Findings

Preroughening transition can be continuous or discontinuous.

Charged mixture behaves as an insulator at the second-order preroughening point.

Metallic behavior occurs below and above the preroughening temperature.

Abstract

Elaborating on previous theoretical treatments of the roughening transition, we provide the exact mapping of a surface model which undergoes both roughening and preroughening onto a mixture of unit and double charges living on the square lattice. Depending on the model parameters, the preroughening transition of the surface can be either continuous or discontinuous. Using the surface temperature as a control parameter, the dual Coulomb gas accordingly undergoes two consecutive phase transitions through equilibrium phases whose dielectric behavior is analysed in terms of Monte Carlo simulation and exact finite-size calculations. Right at the preroughening point of the surface model, the charged mixture behaves like an electric insulator (provided preroughening is second-order), while showing metallic behavior below and above that temperature, at least up to the roughening temperature where the conventional metal-insulator transition occurs.