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.

翻译：在先前的一篇论文（arXiv:2510.19746）中，我们从可恢复系统的角度研究了正方格点 ${\mathbb Z}^2$ 上的最大硬核模型。本文将此项研究推广至三角格点 ${\mathbb A}$ 的情形。我们获得了以下结果：（1）推导了 ${\mathbb A}$ 上相关可恢复系统容量的界；（2）证明了在高活度区域吉布斯测度的非唯一性；（3）在足够低的活度值下刻画了极值周期吉布斯测度的特征。