The maximal hard-core model on the triangular lattice

Abstract

The well-known hard-core model on the triangular lattice $\mathbb{A}$ is an interaction model defined on the independent sets of the lattice, parameterized by an activity parameter $\lambda >0$. In this work, we consider an extension of this model to maximal independent sets, which we call the maximal hard-core model. We show that in the high-activity regime ($\lambda >10^6$), the model admits at least two Gibbs measures on maximal independent sets in $\mathbb{A}$. In the low-activity regime ($\lambda$ close to $0$), we apply Pirogov-Sinai theory to characterize extremal periodic Gibbs measures of the model. Finally, we derive bounds on the capacity of a recoverable system on the lattice associated with the maximal hard-core model.

v2: Improved bound on the activity above which multiple phases occur in the high-activity regime. Extended abstract of this paper appears in Proc. 2026 IEEE International Symposium on Information Theory; v3: Rewritten for journal submission, main results unchanged