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.
We studied the continuous phase transition between the active and the absorbing state of the Ziff-Gulari-Barshad (ZGB) model. Through Monte Carlo simulations we determined all the moments of the order parameter up to fourth order and their ratios at the critical point. We show that the ratios we found are in agreement with those of the contact and pair contact processes in two dimensions, which give support to the idea that the ZGB model is in the directed percolation universality class in (2+1) dimensions.
We performed Monte Carlo simulations considering two different models for antiferromagnetic small particles with Ising spins. The spins of the particle are disposed at the sites of the two dimensional arrays with coordination numbers z = 4 and z = 6, around a central spin. The core spins interact antiferromagnetically and the spins at the surface of the particle are disordered. In the first model, we consider an antiferromagnetic core surrounded by a disordered surface of the spin-glass type. In the second model, the core is still antiferromagnetic, but some bonds at the surface are broken. We determined the hysteresis curves, the zero-field-cooling (ZFC) and field-cooling (FC) curves. We have shown that the model with a disordered surface of the spin-glass type fits better the experimental measurements determined for the antiferromagnetic nanoparticles.Recently, the antiferromagnetic small particles have received great attention due to their special behavior in the presence of external magnetic fields. For these particles, the traditional analysis of the antiferromagnetism based on a division of the lattice in two or more interpenetrating sublattices, can not be applied due to the lack of symmetry. The finite size effects are inherent to these small particles, and the observed reduction in the coordination number of the surface spins causes fundamental changes in the magnetic order of the whole particle [1,2].Recent experiments [3,4,5] are consistent with the idea that these small particles are formed by a core, where the spins interact antiferromagnetically, and it is surrounded by a magnetic disordered shell. The disorder of the spins at the surface induces a weak ferromagnetic ordering of the spins in the antiferromagnetic core. This behavior has been observed in ferrimagnetic nanoparticles [1].In this work we report some results on the magnetic properties of the antiferromagnetic small particles through Monte Carlo simulations in square and hexagonal lattices. In this study we considered an Ising spin model to describe the magnetic properties of the antiferromagnetic small particle. We also take two different types of disorder at the surface of the particle. In the first case the disorder is of the spin-glass type, while in the second case, we take some broken bonds at the surface.Our model for the small particle consists of a twodimensional arrangement of spins, disposed in concentric shells of the square and hexagonal lattices [6]. We assume that the small particle has a large uniaxial anisotropy, and the spins can point only in a single direction. We considered particles with six shells, where the ratio between the surface and core spins is around 0.30. The Hamiltonian model for the antiferromagnetic particle is written aswhere H is the external magnetic field, and J ij is the exchange interaction between pairs of nearest neighbor spins. The spin variables are the Ising ones with the values σ i = ±1. J ij assumes the value J ij = J, with J < 0, when σ i and σ j are spins in the core of the particle. The ...
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