Absence of Dipole Glass Transition for Randomly Dilute Classical Ising Dipoles

Dilute dipolar systems in three dimensions are expected to undergo a spin glass transition as the temperature decreases. Contrary to this, we find from Wang-Landau Monte Carlo simulations that at low concentrations $x$, dipoles randomly placed on a cubic lattice with dipolar interactions do not undergo a phase transition. We find that in the thermodynamic limit the ``glass'' transition temperature $T_g$ 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 ($x=20$).