Monte Carlo study of a Heisenberg antiferromagnet on an fcc lattice with and without dilution

A Monte Carlo simulation is performed of a Heisenberg model with nearest-neighbor antiferromagnetic interaction. It is carried out on a fcc lattice of size n×n×n unit cells, where n=4,6, and 8 (4n³ spins), with a fraction (x) of the sites occupied by N spins. This model which is random for $x<1$, on a frustrated lattice, is related to nonconducting spinglasses, such as Cd_1-xMnₓTe. For x=0.5 and 1, we calculated the following quantities: (i) the specific heat C, (ii) $q(t)={N}^{{-}1}{Σ}{i}^{}〈{{{→}}{S}}ᵢ(0)·{}{{{→}}{S}}ᵢ(t)〉$, and (iii) the relaxation time (${τ}$) associated with $q(t)$. For $x=1$, a singularity in $C$ versus the temperature seems to develop at $T{}{0.4J}{{k}B}$, which becomes sharper as $N$ becomes larger, and ${τ}$ seems to diverge as $T{→}{0.4J}{{k}B}$ also. Furthermore, additional results for systems of $8×{}8×{}n$ cells ($256n$ spins) for $n=2,4, and 8$, show that the peak in $C$ becomes rounded as $n$ decreases. For $x=0.5$, $C$ seems to be smooth in $T$ and independent of $N$, and ${τ}{~}{T}^{{-}3}$ which indicates that there is no transition for $T{≠}0$. Thus this model seems to lack some essential ingredient to describe the paramagnetic to spin-glass transition seen experimentally in systems such as ${Cd}_{1{-}x}{Mn}ₓTe$.