Surface state on first-order ferroelectrics

Extensive Monte Carlo simulations are used to investigate the stability of the ferromagneticground state in three-dimensional systems of Ising dipoles with added quenched disorder. These systemsmodel 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 renormalisationgroup calculation. These functions include logarithmic corrections to the expected mean field behavioursince the system is in its upper critical dimension. Scaled data confirm the validity of the finite-size scalingdescription and results are compared with subsequent analysis of weakly disordered systems. A disordertemperaturephase diagram displays the preservation of the ferromagnetic ground state with the additionof small amounts of disorder, suggesting the irrelevance of weak disorder in these systems.