Monte Carlo study of the antiferromagnetical Ising model on a centred honeycomb lattice

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_\rm A - A and J_\rm A - B in this lattice. Our study is focused on how the ratio of J_\rm A - B to J_\rm 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_\rm A - B to J_\rm A - A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio J_\rm A - B / J_\rm A - A. This work is helpful for studying the phase transition problem of crystals composed of compounds.