Dipolar interactions and thermal stability of two-dimensional   nanoparticle arrays
  We show results of Monte Carlo simulations of an array of monodispersed magnetic monodomain particles, in a square lattice with dipolar interactions and perpendicular uniaxial anisotropy. We first show the equilibrium phase diagram of the system, which shows three phases, superparamagnetic (SP), out-of-plane antiferromagnetic and in-plane antiferromagnetic with a reorientation transition between the last two. We then employ a recently introduced time quantified Monte Carlo method to study the relaxation of autocorrelations of the particle array for different ratios of dipolar to anisotropy energies. In the non-interacting case we show that relaxation is exponential in time with characteristic times obeying a classic result by Brown. When dipolar interactions are switched on, the relaxation is very well described by stretched exponential forms in the whole time window and in both the SP and ordered phases. Relaxation times still obey a nearly Arrhenius behaviour, with a single effective energy barrier that decreases as the dipolar interaction increases, a result that must be interpreted within the dynamics protocol. No signs of glassy behaviour were found, in agreement with the absence of disorder in the model system. 
Daniel A Stariolo and Orlando V. Billoni