Phase transitions in site diluted systems of Ising dipoles

By Monte Carlo simulations, we study dilute systems of Ising magnetic dipoles on simple cubic lattices. Dipoles are restricted to point along the $z$ axis and are randomly placed in a fraction $x$ of the $L^3$ sites of the lattice. For $x_c < x\le1$ where $x_c \simeq 0.6$ we find a thermally driven second order transition between a paramagnetic and a dipolar antiferromagnetic (AF) phase at a temperature $T_o$ which can be fitted by $k_B T_o/ \varepsilon_d \simeq 4.3 (x-x_c)^{0.6}$, where $\varepsilon_d$ is a nearest neighbor dipole-dipole interaction energy. We explore whether an equilibrium spin glass phase exists for $x < x_c$. To this end, we study the spin glass overlap parameter $q$ between equilibrium configurations which we obtain from tempered Monte Carlo simulations for systems of $N$ dipoles in the range $40 \le N \le 500$. For $x < x_c$ we find no AF phase transition. However, we observe rather large AF correlation lengths at low temperatures for $0.2^{1/2}$. Their shape does not change appreciably with $N$. For smaller values of $x$, for which previous results exists, we have not been able to obtain clear cut results.