  We study the critical behavior and the out-of-equilibrium dynamics of a
two-dimensional Ising model with non-static interactions. In our model, bonds
are dynamically changing according to a majority rule depending on the set of
closest neighbors of each spin pair, which prevents the system from ordering in
a full ferromagnetic or antiferromagnetic state. Using a parallel-tempering
Monte Carlo algorithm, we find that the model undergoes a continuous phase
transition at finite temperature, which belongs to the Ising universality
class. The properties of the bond structure and the ground-state entropy are
also studied. Finally, we analyze the out-of-equilibrium dynamics which
displays typical glassy characteristics at a temperature well below the
critical one.
