  Inspired by the program of discrete holography, we show that
Jackiw-Teitelboim (JT) gravity on a hyperbolic tiling of Euclidean AdS$_2$
gives rise to an Ising model on the dual lattice, subject to a topological
constraint. The Ising model involves an asymptotic boundary condition with
spins pointing opposite to the magnetic field. The topological constraint
enforces a single domain wall between the spins of opposite direction, with the
topology of a circle. The resolvent of JT gravity is related to the free energy
of this Ising model, and the classical limit of JT gravity corresponds to the
Ising low-temperature limit. We study this Ising model through a Monte Carlo
approach and a mean-field approximation. For finite truncations of the infinite
hyperbolic lattice, the map between both theories is only valid in a regime in
which the domain wall has a finite size. For the extremal cases of large
positive or negative coupling, the domain wall either shrinks to zero or
touches the boundary of the lattice. This behavior is confirmed by the
mean-field analysis. We expect that our results may be used as a starting point
for establishing a holographic matrix model duality for discretized gravity.
