  We construct a model of short-range interacting Ising spins on a
translationally invariant two-dimensional lattice that mimics a reversible
circuit that multiplies or factorizes integers, depending on the choice of
boundary conditions. We prove that, for open boundary conditions, the model
exhibits no finite-temperature phase transition. Yet we find that it displays
glassy dynamics with astronomically slow relaxation times, numerically
consistent with a double exponential dependence on the inverse temperature. The
slowness of the dynamics arises due to errors that occur during thermal
annealing that cost little energy but flip an extensive number of spins. We
argue that the energy barrier that needs to be overcome in order to heal such
defects scales linearly with the correlation length, which diverges
exponentially with inverse temperature, thus yielding the double exponential
behavior of the relaxation time.
