  A graphical representation based on duplication is developed that is suitable
for the study of Ising systems in external fields. Two independent replicas of
the Ising system in the same field are treated as a single four-state
(Ashkin-Teller) model. Bonds in the graphical representation connect the
Ashkin-Teller spins. For ferromagnetic systems it is proved that ordering is
characterized by percolation in this representation. The representation leads
immediately to cluster algorithms; some applications along these lines are
discussed.
