  A cluster Monte Carlo method for systems of classical spins with purely
dipolar couplings is presented. It is tested and applied for finite arrays of
perpendicular Ising dipoles on the triangular lattice. This model is a
modification with long-range interactions of the geometrically frustrated Ising
antiferromagnet. From measurements of integrated autocorrelation times for
energy, magnetization and staggered magnetizations, a high efficiency of the
cluster Monte Carlo (MC) algorithm compared to a single-spin-flip algorithm is
found. For the investigated model, a finite temperature transition is found
which is characterized by a peak in the specific heat and in the staggered
susceptibilities.
