Low-temperature spin-glass behavior in a diluted dipolar Ising system

Abstract

Using Monte Carlo simulations, we study the character of the spin-glass (SG) state of a site-diluted dipolar Ising model. We consider systems of dipoles randomly placed on a fraction $x$ of all ${L}^{3}$ sites of a simple cubic lattice that point up or down along a given crystalline axis. For $x\ensuremath{\lesssim}0.65$ these systems are known to exhibit an equilibrium spin-glass phase below a temperature ${T}_{\mathrm{sg}}\ensuremath{\propto}x$. At high dilution and very low temperatures, well deep in the SG phase, we find spiky distributions of the overlap parameter $q$ that are strongly sample dependent. We focus on spikes associated with large excitations. From cumulative distributions of $q$ and a pair correlation function averaged over several thousands of samples we find that, for the system sizes studied, the average width of spikes, and the fraction of samples with spikes higher than a certain threshold, does not vary appreciably with $L$. This is compared with the behavior found for the Sherrington-Kirkpatrick model.