  Ising or Potts models of ferromagnetism have been widely used to describe
locally interacting social or economic systems. We consider a related model,
introduced by Sznajd to describe the evolution of consensus in a society. In
this model, the opinion or state of any spins can only be changed through the
influence of neighbouring pairs of similarly aligned spins. Such pairs can
polarize their neighbours. We show that, assuming the global dynamics evolve in
a synchronous manner, the two-state Sznajd model exhibits a non-monotonically
decreasing overall orientation that has a maximum value when the system is
subject to a finite value of noise. Reinterpreting the model in terms of
opinions within a society we predict that consensus can be increased by the
addition of an appropriate amount of random noise. These features are explained
by the presence of islands of complete orientation that are stable in the
absence of noise but removed via the presence of added noise.
