Entropic commensurate-incommensurate transition

TL;DR

This paper studies a minimal tiling model with extensive ground state entropy, revealing a transition from quasiperiodic to disordered phases via a sequence of periodic arrangements, analogous to the Frenkel-Kontorova model.

Contribution

It introduces a minimal tiling model exhibiting entropic transitions and draws an analogy with the Frenkel-Kontorova model, highlighting temperature-driven phase changes.

Findings

Transition involves a sequence of periodic arrangements

Ground state entropy is extensive

Transition mechanism resembles Frenkel-Kontorova model

Abstract

The equilibrium properties of a minimal tiling model are investigated. The model has extensive ground state entropy, with each ground state having a quasiperiodic sequence of rows. It is found that the transition from the quasiperiodic ground state to the high temperature disordered phase proceeds through a sequence of periodic arrangements of rows, in analogy with the Frenkel-Kontorova model, but with temperature playing the role of the strength of the substrate potential.