Extensive Monte Carlo simulations are used to investigate the stability of the ferromagnetic ground state in three-dimensional systems of Ising dipoles with added quenched disorder. These systems model the collective ferromagnetic order observed in various systems with dipolar long-range interactions. The uniaxial dipolar spins are arranged on a face-centred cubic lattice with periodic boundary conditions. Finite-size scaling relations for the pure dipolar ferromagnetic system are derived by a renormalisation group calculation. These functions include logarithmic corrections to the expected mean field behaviour since the system is in its upper critical dimension. Scaled data confirm the validity of the finite-size scaling description and results are compared with subsequent analysis of weakly disordered systems. A disorder-temperature phase diagram displays the preservation of the ferromagnetic ground state with the addition of small amounts of disorder, suggesting the irrelevance of weak disorder in these systems.
Klopper, A. V., Robler, U. K., & Stamps, R. (2006). Effect of weak disorder on the ground state of uniaxial dipolar spin systems in the upper critical dimension. The European Physical Journal B, 50(1/2), 45-50. https://doi.org/10.1140/epjb/e2006-00123-0