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 $n\times n\times n$ unit cells, where $n=4,6, \mathrm{and} 8$ ($4n^3$ spins), with a fraction ($x$) of the sites occupied by $N$ spins. This model which is random for $x<\mathrm{}1\mathrm{}$, on a frustrated lattice, is related to nonconducting spinglasses, such as ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$. For $x=0.5\mathrm{} \mathrm{and} 1$, we calculated the following quantities: (i) the specific heat $C$, (ii) $q\mathrm{}\left(t\right)=N^{-1\mathrm{}}\Sigma i^{}〈{\overrightarrow{\mathrm{S}}}_i\mathrm{}\left(0\right)\mathrm{}·{\overrightarrow{\mathrm{S}}}_i\mathrm{}\left(t\right)\mathrm{}〉$, and (iii) the relaxation time ($\tau$) associated with $q\mathrm{}\left(t\right)\mathrm{}$. For $x=1\mathrm{}$, a singularity in $C$ versus the temperature seems to develop at $T\cong \frac{0.4J}{k_B}$, which becomes sharper as $N$ becomes larger, and $\tau$ seems to diverge as $T\to \frac{0.4J}{k_B}$ also. Furthermore, additional results for systems of $8\times 8\times n$ cells ($256n$ spins) for $n=2,4, \mathrm{and} 8$, show that the peak in $C$ becomes rounded as $n$ decreases. For $x=0.5\mathrm{}$, $C$ seems to be smooth in $T$ and independent of $N$, and $\tau \sim T^{-3\mathrm{}}$ which indicates that there is no transition for $T\ne 0$. Thus this model seems to lack some essential ingredient to describe the paramagnetic to spin-glass transition seen experimentally in systems such as ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$.