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We studied a layered mixed-spin Ising model, with spins σ = 1/2 and S = 1, distributed on the sites of a hexagonal lattice. For this spin arrangement, any spin at one lattice site has two nearest-neigbor spins of the same type, and four of the other type. We assumed that the exchange interaction between spins σ and S is antiferromagnetic, with the value J1. J2 is the exchange interaction between two nearest neighbor σ spins, and J3 is the coupling between two nearest neighbor S spins. We also considered a single-ion crystal-field contribution D to the S sites. We performed mean-field calculations and Monte Carlo simulations to determine the compensation point of the model. We have shown that a compensation point can be present for any positive value of D. We have also found a negative lower bound for D, below which a compensation point can not appear. For each value of D, we determined the range of values of the J2 and J3 couplings for which a compensation point is realizable.

We studied a monomer-dimer catalytic surface reaction model of the type 1 / 2A(2)+BA-->A2B, where interactions between nearest-neighbor species and the temperature of the catalyst are considered. Through Monte Carlo simulations we determined the phase diagram of the model in the plane temperature versus partial pressure of the BA molecules in its gaseous phase. We found that the transition between the A-poisoned state and the active one is always continuous and the associated critical exponents are in the same universality class of the directed percolation (DP). On the other hand, the transition from the active state to the BA-poisoned one changes from continuous to first order for a given temperature value. The critical exponents of the continuous branch belong also to the DP universality class. For a small range of values of the partial pressure of BA and very low temperatures, we observe the formation of an inactive sublattice structure inside the active phase.

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