We investigate the density of states (DOS) in an antiferromagnetic spin-system on a square lattice described by the Blume-Capel (BC) model. We use a new and very efficient simulation method, proposed by Wang and Landau, in which we estimate very precisely DOS by sampling in the space of energy. Then we calculate the thermodynamical averages like internal energy, free energy, specific heat and entropy. The BC model exhibits multicritical behaviour such as first- or second-order transitions and tricritical points. It is known that the ground state of the model can exhibit two kinds of staggered antiferromagnetic phases: AF1 (two interpenetrating lattices with S = -1 and S = 1) and AF2 (S = -1 and S = 0 for H < 0; S = 1 and S = 0 for H > 0). We analyze the coexistence of such phases at finite temperatures and determine border lines between them. To understand the microscopic nature of such boundaries we present also some results obtained with the standard Monte Carlo method.
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