Monte Carlo simulations of the ${\rm LiHo_xY_{1-x}F_4}$ diluted dipolar magnet

Recent intriguing experimental results on ${\rm LiHo_xY_{1-x}F_4}$, a diluted dipolar magnet, along with new analytical insights, suggest that neither a mean-field treatment nor simulations using simplified versions of the underlying Hamiltonian adequately describe these materials. Not only does this imply that novel disordering mechanism might be present, it requires a detailed numerical analysis that incorporates all terms in the Hamiltonian. We present large-scale Monte Carlo simulations of the diluted dipolar magnet with competing interactions on a ${\rm LiHo}$ lattice with the inclusion of a random field term. For low concentrations of ${\rm Ho}$ atoms we reproduce the peculiar linear dependence of the transition temperature as a function of the random-field strength found in recent experimental results by Silevich {\em et al}.~[Nature {\bf 448}, 567 (2007)]. We then find a zero-temperature phase transition between the ferromagnetic and quasi-spin-glass phases, suggesting that it is the underlying spin-glass phase that dictates the above linear dependence of $T_c$ on the random field. For large concentrations we recover the quadratic dependence of the critical temperature as a function of the random field strength.