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

## Abstract

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 Cd1-xMnxTe. For x=0.5 and 1, we calculated the following quantities: (i) the specific heat C, (ii) q (t)=N-1iSi(0)Si(t), and (iii) the relaxation time () associated with q (t). For x=1, a singularity in C versus the temperature seems to develop at T0.4JkB, which becomes sharper as N becomes larger, and seems to diverge as T0.4JkB 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 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 Cd1-xMnxTe. © 1983 The American Physical Society.