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：在先前的工作(arXiv:2510.19746)中，我们从可恢复系统的角度研究了正方晶格${\mathbb Z}^2$上的最大硬核模型。本文将此研究拓展至三角晶格${\mathbb A}$的情形，得到以下结果：(1) 我们导出了${\mathbb A}$上相关可恢复系统容量的界；(2) 我们证明了高活度区域中吉布斯测度的非唯一性；(3) 我们刻画了充分低活度下的极值周期吉布斯测度。