The disorder-driven phase transition of the RFIM is observed using exact ground-state computer simulations for hyper cubic lattices in d = 5, 6, 7 dimensions. Finite-size scaling analyses are used to calculate the critical point and the critical exponents of the specific heat, magnetization, susceptibility and of the correlation length. For dimensions d = 6, 7 which are larger or equal to the assumed upper critical dimension, du = 6, mean-field behaviour is found, i.e. α = 0, β = 1/2, γ = 1, ν = 1/2. For the analysis of the numerical data, it appears to be necessary to include recently proposed corrections to scaling at and beyond the upper critical dimension.

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We study the correlated-disorder driven zero-temperature phase transition of the Random-Field Ising Magnet using exact numerical ground-state calculations for cubic lattices. We consider correlations of the quenched disorder decaying proportional to r a , where r is the distance between two lattice sites and a < 0. To obtain exact ground states, we use a well established mapping to the graph-theoretical maximum-flow problem, which allows us to study large system sizes of more than two million spins. We use finite-size scaling analyses for values a = {−1, −2, −3, −7} to calculate the critical point and the critical exponents characterizing the behavior of the specific heat, magnetization, susceptibility and of the correlation length close to the critical point. We find basically the same critical behavior as for the RFIM with δ-correlated disorder, except for the finite-size exponent of the susceptibility and for the case a = −1, where the results are also compatible with a phase transition at infinitesimal disorder strength. A summary of this work can be found at the papercore database www.papercore.org.

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