Recoverable systems and the maximal hard-core model on the triangular lattice
This is an incremental extension of prior work to a different lattice geometry, providing theoretical results for statistical mechanics models.
The paper extends the study of recoverable systems and the maximal hard-core model from the square lattice to the triangular lattice, deriving capacity bounds, proving non-uniqueness of Gibbs measures at high activity, and characterizing extremal periodic Gibbs measures at low activity.
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.