  The Bethe lattice Ising model -- a classical model of statistical mechanics
for the phase transition -- provides a novel and intuitive understanding of the
prototypical relationship between tensor networks and Anti-de Sitter
(AdS)/conformal field theory (CFT) correspondence. After analytically
formulating a holographic renormalization group for the Bethe lattice model, we
demonstrate the underlying mechanism and the exact scaling dimensions for the
power-law decay of boundary spin correlations by introducing the relation
between the lattice network and an effective Poincare metric on a unit disk. We
compare the Bethe lattice model in the high-temperature region with a scalar
field in AdS$_2$, and then discuss its more direct connection to the p-adic
AdS/CFT. In addition, we find that the phase transition in the interior induces
a crossover behavior of boundary spin correlations, depending on the depth of
the corresponding correlation path.
