A finite-temperature liquid-quasicrystal transition in a lattice model

TL;DR

This paper investigates a two-dimensional lattice tiling model with Wang tiles, revealing a finite-temperature phase transition from disorder to quasi-periodic order, and characterizes its critical behavior through critical exponents.

Contribution

It introduces a lattice model exhibiting a liquid-quasicrystal transition at finite temperature and analyzes its critical properties, which was not previously established.

Findings

Identified a disorder to quasi-periodicity phase transition at finite temperature.

Extracted critical exponents consistent with hyper-scaling.

Demonstrated the existence of a liquid-quasicrystal phase transition in a lattice model.

Abstract

We consider a tiling model of the two-dimensional square-lattice, where each site is tiled with one of the sixteen Wang tiles. The ground states of this model are all quasi-periodic. The systems undergoes a disorder to quasi-periodicity phase transition at finite temperature. Introducing a proper order-parameter, we study the system at criticality, and extract the critical exponents characterizing the transition. The exponents obtained are consistent with hyper-scaling.