Absence of Dipole Glass Transition for Randomly Dilute Classical Ising Dipoles

Randomly dilute dipoles with long range dipolar interactions appear in a variety of solid insulating materials. Based on theoretical studies of spin glasses with long range interactions, one would expect such dilute dipolar systems to undergo a spin glass-like transition as the temperature decreases. However, there has been no experimental evidence for such a transition in very dilute systems. One example where such a transition has not been definitively observed is two level systems that dominate the physics of glasses at low temperatures. Another is LiHo$_x$Y$_{1-x}$F$_4$ with $x=4.5\%$. We have investigated the absence of a phase transition in dilute dipolar glasses. Using Wang-Landau Monte Carlo simulations, we show that at low concentrations $x$, dipoles randomly placed on a cubic lattice with dipolar interactions do not undergo a phase transition as the temperature decreases. We define a characteristic ``glass'' temperature $T_g$ as the temperature where the distribution $P(q,T)$ is flattest. $q$ is the overlap order parameter. We find that in the thermodynamic limit $T_g$ goes to zero as $1/\sqrt{N}$ where $N$ is the number of dipoles. The entropy per particle at low temperatures is larger for lower concentrations ($x=4.5\%$) than for higher concentrations ($x=20\%$).