  The multicanonical method has been proven powerful for statistical
investigations of lattice and off-lattice systems throughout the last two
decades. We discuss an intuitive but very efficient parallel implementation of
this algorithm and analyze its scaling properties for discrete energy systems,
namely the Ising model and the 8-state Potts model. The parallelization relies
on independent equilibrium simulations in each iteration with identical
weights, merging their statistics in order to obtain estimates for the
successive weights. With good care, this allows faster investigations of large
systems, because it distributes the time-consuming weight-iteration procedure
and allows parallel production runs. We show that the parallel implementation
scales very well for the simple Ising model, while the performance of the
8-state Potts model, which exhibits a first-order phase transition, is limited
due to emerging barriers and the resulting large integrated autocorrelation
times. The quality of estimates in parallel production runs remains of the same
order at same statistical cost.
