First Order Phase Transition in a Model of Quasicrystals

TL;DR

This paper introduces a 2D lattice model for quasicrystals with hard cores and soft interactions, demonstrating a first order phase transition between disordered and quasicrystalline phases through Monte Carlo simulations.

Contribution

It presents a novel lattice model for quasicrystals incorporating aperiodic tilings and soft interactions, revealing phase transition behavior.

Findings

First order phase transition observed

Transition occurs between disordered and quasicrystalline phases

Monte Carlo simulations confirm the phase change

Abstract

We introduce a family of two-dimensional lattice models of quasicrystals, using a range of square hard cores together with a soft interaction based on an aperiodic tiling set. Along a low temperature isotherm we find, by Monte Carlo simulation, a first order phase transition between disordered and quasicrystalline phases.