  We analyze boundary spin correlation functions of the hyperbolic-lattice
Ising model from the holographic point of view. Using the
corner-transfer-matrix renormalization group (CTMRG) method, we demonstrate
that the boundary correlation function exhibits power-law decay with
quasi-periodic oscillation, while the bulk correlation function always decays
exponentially. On the basis of the geometric relation between the bulk
correlation path and distance along the outer edge boundary, we find that
scaling dimensions for the boundary correlation function can be well explained
by the combination of the bulk correlation length and background curvatures
inherent to the hyperbolic lattice. We also investigate the cutoff effect of
the bond dimension in CTMRG, revealing that the long-distance behavior of the
boundary spin correlation is accurately described even with a small bond
dimension. In contrast, the sort-distance behavior rapidly loses its accuracy.
