Abstract The simple but realistic model described by a Heisenberg Hamiltonian with nearest neighbours and next nearest neighbours interactions in an external magnetic field was investigated by use of the Monte Carlo method. Three-dimensional vector spins of length 5 2 were distributed randomly on a fcc lattice. Different concentrations of spins, x = 0.05, 0.10,…,0.90, were studied. For low concentrations, simulated samples contained about 1000 spins. For higher values of x the size of system was about 8000. All the computations were done for high external magnetic fields of around 3 T. During simulation, physical quantities such as magnetization, energy, specific heat and magnetic susceptibility were determined. The results for magnetization differ for the zero-field-cooled (ZFC) and field-cooled (FC) cases for the whole range of concentrations. This difference, also typical for experimental data, seems to vanish after longer simulation. From critical temperatures for computer simulated magnetization, the magnetic phase diagram was obtained and compared to experimental data for Cd 1- x Mn x Te. Concentration dependent results for magnetization, specific heat and magnetic susceptibility allowed one to distinguish three different regions for the simulated system: x ≤ 0.20, 0.30 ≤ x ≤ 0.60, 0.70 ≤ x ≤ 0.90.