Recoverable systems and the maximal hard-core model on the triangular lattice

TL;DR

This paper extends the study of recoverable systems and the maximal hard-core model from the square lattice to the triangular lattice, deriving capacity bounds, analyzing Gibbs measure uniqueness, and characterizing extremal measures.

Contribution

It introduces new capacity bounds and characterizations of Gibbs measures for the maximal hard-core model on the triangular lattice, expanding prior work on the square lattice.

Findings

Derived bounds on the capacity of recoverable systems on the triangular lattice.

Demonstrated non-uniqueness of Gibbs measures at high activity levels.

Characterized extremal periodic Gibbs measures at low activity levels.

Abstract

In a previous paper (arXiv:2510.19746), we have studied the maximal hard-code model on the square lattice ${\mathbb Z}^2$ from the perspective of recoverable systems. Here we extend this study to the case of the triangular lattice ${\mathbb A}$. The following results are obtained: (1) We derive bounds on the capacity of the associated recoverable system on ${\mathbb A}$; (2) We show non-uniqueness of Gibbs measures in the high-activity regime; (3) We characterize extremal periodic Gibbs measures for sufficiently low values of activity.