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We have used the Curie–Weiss mean-field approximation to study the effects of the random single-ion anisotropy and random magnetic field in the phase diagram and thermodynamic properties of the spin-5/2 Blume–Capel model. The phase diagrams have been presented in the temperature T ∕ J versus strength random single-ion anisotropy D ∕ J and strength random magnetic field h ∕ J planes. The magnetization dependence was plotted as a function of temperature and the strength single-ion anisotropy. These diagrams showed that the different phase transition types, first-or second-order between the ferromagnetic and paramagnetic phases, are dependent on the random parameters. Therefore, within these conditions, the model presents tricritical behavior. • Several phase diagrams were obtained for the spin-5/2 Blume–Capel model. • The influence of the random single-ion anisotropy and magnetic field was examined for the system. • First- and second-order phase transition lines were found. • The tricritical behavior was examined. [ABSTRACT FROM AUTHOR]

In this work, we have performed Monte Carlo simulations to study a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on a square lattice with two different random single-ion anisotropies. This lattice is divided in two interpenetrating sublattices with spins S A = 1 in the sublattice A and S B = 3 ∕ 2 in the sublattice B . The exchange interaction between the spins on the sublattices is antiferromagnetic ( J < 0 ). We used two random single-ion anisotropies, D i A and D j B , on the sublattices A and B , respectively. We have determined the phase diagram of the model in the critical temperature T c versus strength of the random single-ion anisotropy D plane and we shown that it exhibits only second-order phase transition lines. We also shown that this system displays compensation temperatures for some cases of the random single-ion distribution. [ABSTRACT FROM AUTHOR]

We have considered a generalized version of a model consisting of self-propelled particles, where the speed is treated as an independent stochastic variable described by a Gamma-distribution, and the motion direction is adjusted in according to two behavioral rules: repulsion and orientation. We used the finite-size scaling theory to estimate the static critical exponents β , γ and ν as a function of the density ρ . We have obtained different values of the critical exponents for different values of the density ρ . [ABSTRACT FROM AUTHOR]

Abstract We have studied the effects of the random transverse single-ion anisotropy in the phase diagram and in the thermodynamic properties of the spin − 1 Blume–Capel quantum model, which has been used the approach the mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. The phase diagrams were obtained in the temperature τ = k B T ∕ z J versus single-ion anisotropy δ x = D x ∕ z J plane for several values of δ y = D y ∕ z J , p and q. The results show that there is a tricritical behavior only in the range of δ y given by − 0. 048 ≤ δ y < 0. 5. This behavior is shown again by the curves of the magnetization m as a function of temperature τ with corresponding values of δ y , p and q. Highlights • Several phase diagrams were obtained for the spin-1 Blume–Capel quantum model. • The influence of the random single-ion anisotropies was examined for the system. • First- and second-order phase transition lines were found. • The tricritical behavior was examined. [ABSTRACT FROM AUTHOR]

We have studied the effects of two different random single-ion anisotropies in the phase diagram and on the critical properties of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system. We employed the mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. We have used the Landau expansion of the free energy in the order parameter to describe the phase diagram. We have shown that the phase diagram temperature as function of random single-ion anisotropy displays tricritical behavior. We also investigated the existence and dependence of a compensation temperature on random single-ion anisotropies. The critical and compensation temperatures increase with increasing of the random single-ion anisotropies values. [ABSTRACT FROM AUTHOR]

We study the mixed spin-1 and spin-3/2 ferrimagnetic Ising system under the effect of different random crystal-fields within the mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. The phase diagrams are obtained in the plane of critical temperature versus random crystal-field, showing a tricritical behavior with second-order transition lines separating the first-order transition lines by tricritical points. [ABSTRACT FROM AUTHOR]