# Sturmian ground states in classical lattice-gas models

## TL;DR

This paper introduces classical lattice-gas models with ground states characterized by Sturmian sequences, constructed via irrational rotations, and uniquely defined by minimal forbidden patterns, exemplified by Fibonacci sequences.

## Contribution

It presents the first examples of non-frustrated, infinite-range, one-dimensional lattice-gas models with Sturmian ground states defined by minimal forbidden patterns.

## Key findings

- Ground states are Sturmian sequences from irrational rotations.
- Minimal forbidden patterns uniquely define Sturmian sequences.
- Models exemplify Fibonacci sequences as ground states.

## Abstract

We construct for the first time examples of non-frustrated, two-body, infinite-range, one-dimensional classical lattice-gas models without periodic ground-state configurations. Ground-state configurations of our models are Sturmian sequences defined by irrational rotations on the circle. We present minimal sets of forbidden patterns which define Sturmian sequences in a unique way. Our interactions assign positive energies to forbidden patterns and are equal to zero otherwise. We illustrate our construction by the well-known example of the Fibonacci sequences.