Monte-Carlo simulations for two-stage percolation transition of the enhanced trees

We investigate the bond percolation problem on the enhanced binary tree (EBT). The EBT is given by adding intra-generation links to the binary tree. The EBT belongs to the class of {\it nonamenable graphs} (NAGs), and percolations on NAGs are predicted to show two-stage transition through three distinct phases according to open bond probability $p$; (i) {\it nonpercolating phase}: there is no infinite cluster for $0 \le p