  Critical behavior of the Ising model is investigated at the center of large
scale finite size systems, where the lattice is represented as the tiling of
pentagons. The system is on the hyperbolic plane, and the recursive structure
of the lattice makes it possible to apply the corner transfer matrix
renormalization group method. From the calculated nearest neighbor spin
correlation function and the spontaneous magnetization, it is concluded that
the phase transition of this model is mean-field like. One parameter
deformation of the corner Hamiltonian on the hyperbolic plane is discussed.
