Constructing ultra-slow glasses in lattice models for reversible computation*

We construct a two-dimensional lattice model that lacks any finite
temperature phase transition and yet displays relaxation times that
grow as a double exponential of the inverse temperature. The model has
bulk translational invariance, only broken by the presence of the
boundaries. The lattice model is associated to a reversible circuit
that can multiply or factorize integers, depending on the boundary
conditions. When the lattice model reaches its ground state, all
computations are performed without error. The ultra-slow (double
exponential in inverse temperature) glassy dynamics is associated with
the difficulty of the system to heal computational errors that cost
little energy but flip a volumetric number of bits in the system.