Ferromagnetic Ising model on the hierarchical pentagon lattice

Thermodynamic properties of the ferromagnetic Ising model on the hierarchical pentagon lattice is studied by means of the tensor network methods. The lattice consists of pentagons, where 3 or 4 of them meet at each vertex. Correlation functions on the surface of the system up to n = 10 layers are evaluated by means of the time evolving block decimation (TEBD) method, and the power low decay is observed in the high temperature region. The recursive structure of the lattice enables complemental numerical study for larger systems, by means of a variant of the corner transfer matrix renormalization group (CTMRG) method. Calculated spin expectation value shows that there is a mean-field type order-disorder transition at T1 = 1.58 on the surface of the system. On the other hand, the bulk part exhibits the transition at T2 = 2.269. Consistency of these calculated results is examined.