Thermodynamic transition associated with irregularly ordered ground states in a lattice gas model

TL;DR

This paper introduces a 2D lattice gas model with irregularly ordered ground states that are non-periodic and system-size dependent, and suggests a thermodynamic transition linked to this unique ordering.

Contribution

It proposes a novel lattice gas model with irregular ground states and conjectures a related thermodynamic transition supported by duality, phenomenology, and numerical evidence.

Findings

Ground state is irregular and depends on system size.

Entropy density approaches zero in the thermodynamic limit.

Thermodynamic transition is conjectured based on duality and supported by experiments.

Abstract

A two-dimensional lattice gas model is proposed. The ground state of this model with a fixed density is neither periodic nor quasi-periodic. It also depends on system size in an irregular manner. On the other hand, it is ordered in the sense that the entropy density is zero in the thermodynamic limit. The existence of a thermodynamic transition associated with such irregularly ordered ground states is conjectured from a duality relation for a thermodynamic function. This conjecture is supported by a phenomenological argument and numerical experiments.