A Frenkel-Kontorova Model with Two Spring Constants: New Phases and Phase Transitions

TL;DR

This paper investigates a modified Frenkel-Kontorova model with alternating spring constants, revealing new phases and phase transitions, including an unpinned commensurate phase and a transition to an unlocked phase as substrate potential increases.

Contribution

It introduces a novel FK model with two spring constants, showing unique phases and phase transitions not present in the standard model.

Findings

Existence of an unpinned commensurate phase with translational invariance.

Identification of a phase transition on the lattice point in parameter space.

Prediction of a transition to an unlocked commensurate phase with increased substrate potential.

Abstract

A discrete Frenkel-Kontorova model with two alternate spring constants $k_{1}$ and $k_{2}$ is studied. It is found that this model has many surprising behaviours. The continuum version of this model is different from the sine-Gordon equation, which is the continuum version of the standard FK model. More interestingly, it has an unpinned commensurate phase which is translationally invariant. A phase transition takes place on a lattice point in the parameter space. We have also predicted another interesting phase transition in which an unlocked commensurate phase breaking translational invariance will take place as the strength of the substrate potential is increased.