We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B.There exist two different bond energies J_(a-a) and J_(a-b) in this lattice.Our study is focused on how the ratio of J_(a-B) to J_(a-A) influences the critical behaviour of this system by analysing the physical quantities,such as the energy,the order parameter,the specific heat,susceptibility,etc each as a function of temperature for a given ratio of J_(a-b) to J_(a-A).Using these results together with the finite-size scaling method,we obtain a phase diagram for the ratio J_(a-b)/J_(A-A).This work is helpful for studying the phase transition problem of crystals composed of compounds.
