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The dynamic phase transitions are studied, within a mean-field approach, in the kinetic Blume-Emery-Grifftihs model under the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics and the set of the dynamic equations of motion is obtained. The behavior of the time-dependence of the order parameters and the behavior of the average order parameters in a period, which is also called the dynamic order parameters, as a function of the reduced temperature are investigated. The nature (continuous and discontinuous) of transition is characterized by studying the average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. We have found that the behavior of system strongly depends on the interaction parameters and nine main different phase diagram topologies have been obtained. We also calculate the Liapunov exponents to verify the stability of the solutions and the dynamic phase transition points.

In this paper, we propose a single-lane cellular automata (CA) traffic model which takes into account the disorder in the length and the maximal speed of the vehicles (i.e. slow and fast) to study the satisfaction rate of the fast vehicles (i.e. the number of vehicles that run with their desired speed) with open boundary conditions in the case of a chain of one entry; where $\alpha$ is the injecting rate of vehicles independent of their nature and $\beta$ is the extracting rate. The slow vehicles are injected with the conditional probability ${\alpha }_s$, where $0\le {\alpha }_s=\chi \alpha \le \alpha$ and $\chi$ is the concentration of the slow vehicles. It is found that for the low value of the injecting rate $\alpha$ and for the high extraction rate $\beta$, the satisfaction rate takes higher values. It also depends on the concentration of the slow vehicles injected on the road. Furthermore, we have shown that, in the case when $\alpha =\beta$, the satisfaction rate undergoes a transition from the maximal value to the minimal one and it takes a value near to zero in the case of $\alpha >\beta$. We have also found that the satisfaction rate depends strongly on the probability of overtaking, also the phase diagrams ($\alpha ,\beta$) are established for the different values of the slow vehicles concentrations $\chi$.

The phase diagrams of several dipolar Gay–Berne systems are generated using Monte Carlo simulations. Particular emphasis is placed upon the location, order and nature of the liquid crystalline phases observed at high fluid densities. The accuracy of the reaction field method is re-affirmed.

The effect of the position of the off-ramp (way out), on the traffic flow phase transition is investigated using numerical simulations in the one-dimensional cellular automaton traffic flow model with open boundaries using parallel dynamics. When the off-ramp is located between two critical positions i_c1 and i_c2 the current increases with the extracting rate β₀, for β₀<β_0c1, and exhibits a plateau (constant current) for β_0c1<β₀<β_0c2 and decreases with β₀ for β₀>β_0c2. However, the density undergoes two successive first order transitions: from high density to plateau current phase at β₀=β_0c1; and from average density to the low one at β₀=β_0c2. In the case of two off-ramps located respectively at i₁ and i₂, these transitions occur only when i₂-i₁ is smaller than a critical value. Phase diagrams in the (α,β₀), (β,β₀) and (i₁,β₀) planes are established. It is found that the transitions between free traffic (FT), congested traffic (CT) and plateau current (PC) phases are of first order. The first order line transition in (i₁,β₀)-phase diagram terminates by an end point above which the transition disappears.

Within the framework of Pertsev's thermodynamic theory, the equilibrium polarization states and the physical properties of single-domain Pb(Zr_0.35Ti_0.65)O₃ (PZT) thin films epitaxially grown on dissimilar cubic substrates are investigated. The "misfit strain-temperature" phase diagrams are obtained for the films. The presence of stability range of the rhombohedral phase is the characteristic feature of these phase diagrams, which separates the stability ranges of the tetragonal phase and the orthorhombic phase. The coexistence of the rhombohedral phase and the tetragonal phase in PZT film can be explained by Pertsev's theory with the gradient strain case with a suitable stress form.

On the Ising spin systems constructed with four-body interactions, there appears the "spin-pair ordered phase" or "spin-pair glass phase" in a certain temperature. Especially, the random four-body models include the frustration and the spin-pair glass phase appears in those models. This frustration may play an important role of spin-pair glass transitions, similarly to the case of ordinary spin-glass transitions. In this study, we clarify the way to discriminate quantitatively "frustrated unit cells" from "nonfrustrated ones" on the random four-body models. Then we introduce a parameter to control the frustration in the Ising spin systems with random four-body interactions. This parameter enables us to analyze the frustration continuously in many-body models. Thus we have analyzed the phase transitions and obtained phase diagrams using the frustration parameter. These interesting phase diagrams show that there appear the spin-pair ordered phases even on the completely frustrated models. This result is essentially different from the random two-body models, namely spin-glass models (there appears no ferromagnetic phase in the fully frustrated spin-glass models, which correspond to the Villain models).

Inspired from the connection between Lie symmetries and two-dimensional materials, we propose a new statistical lattice model based on a double hexagonal structure appearing in the G₂ symmetry. We first construct an Ising-1/2 model, with spin values σ = ±1, exhibiting such a symmetry. The corresponding ground state shows the ferromagnetic, the antiferromagnetic, the partial ferrimagnetic and the topological ferrimagnetic phases depending on the exchange couplings. Then, we examine the phase diagrams and the magnetization using the mean field approximation (MFA). Among others, it has been suggested that the present model could be localized between systems involving the triangular and the single hexagonal lattice geometries.

An effective field theory with correlations has been used to study the critical behavior of the spin-1 Blume–Capel bilayer Ising model on a square lattice. The effects of the Hamiltonian parameters on thermodynamic quantities and phase diagrams are investigated in detail. We found that the system exhibits the first and the second order transitions as well as tricritical point. Furthermore, we have observed that the change of tricritical point values depends on interaction parameters.

In this paper, the Monte Carlo simulation (MCS) and the mean field approximation (MFA) methods have been used to study the magnetic properties of double perovskite Ba₂CrMoO₆ in the framework of the Ising model, which is important for a better understanding of the magnetic behavior of this material. This compound is constituted of two magnetic cubic sublattices: one occupied by Mo${}^{5+}$ and other occupied Cr${}^{3+}$, the critical exponents and phase diagrams for this compound are determined. The critical behavior, compensation temperature and susceptibility are also determined.

The phase diagrams and temperature dependences of magnetizations in a transverse Ising bilayer film with an antiferromagnetic spin configuration are studied by the uses of the effective-field theory (EFT) with correlations, in order to clarify whether the appearance of a compensation point is possible below the transition temperature in the system. From these investigations, we have found a lot of characteristic phenomena in these properties, when the value of an interlayer coupling takes a large value, such as the reentrant phenomenon free from the disorder-induced frustration and the novel types of magnetization curve with a compensation point.

In this paper, the phase diagrams and magnetizations of a magnetic nanoisland described by the transverse Ising model (TIM) are investigated by the use of the effective-field theory (EFT) with correlations. A lot of characteristic behaviors observed in standard ferrimagnetic materials as well as novel phenomena have been obtained, although the system consists of two finite spin-1/2 layers coupled antiferromagnetically with a negative interlayer coupling.

The phase diagrams and magnetizations of an Ising nanowire with an amorphization are investigated by the use of the effective field theory with correlations. Some characteristic phenomena have been found in them. The reduced total magnetization falls below that of its corresponding crystalline ferromagnetic nanowire. The reentrant phenomena have been obtained, when the value of amorphization $\delta$ becomes larger than a critical value ($\delta =1.0$).

The phase diagrams and the magnetizations in a graphene-like two-dimensional nanoparticle described by the transverse Ising model are investigated by the use of the effective-field theory with correlations. We have found some characteristic behaviors especially for the system with a small transverse field and a small surface exchange interaction, such as the reentrant phenomena.

The A, B and C atoms with spin-1/2, spin-3/2 and spin-5/2 are joined together sequentially on the Bethe lattice in the form of ABCABC$\dots$ to simulate a molecule as a triple mixed-spin system. The spins are assumed to be interacting with only their nearest-neighbors via bilinear exchange interaction parameter in addition to crystal and external magnetic fields. The order-parameters are obtained in terms of exact recursion relations, then from the study of their thermal variations, the phase diagrams are calculated on the possible planes of our system. It is found that the model gives only second-order phase transitions in addition to the compensation temperatures.

The spin-1/2 antiferromagnetic (AFM) Heisenberg model is considered in the mean-field approximation in terms of the spin operators ${Ŝ}_x,{Ŝ}_y$ and ${Ŝ}_z$ in the matrix forms with the introduction of bilinear exchange interaction ($J_{\mu }$), the Dzyaloshinskii–Moriya interaction (DMI) (${\mathrm{\Delta }}_{\mu }$) and external magnetic fields ($H_{\mu }$) into the Hamiltonian in three dimensions. The thermal changes of sublattice magnetizations $M_{\mu }^A$ and $M_{\mu }^B$ are investigated in the isotropic case to identify the critical behaviors displayed by the system. The phase diagrams are illustrated on various planes of system parameters for given coordination numbers $q=3,4$ and 6. In addition, the graphs of the magnetization components in the same directions were drawn against each other and very interesting results were obtained. The model exhibits the ordered phases, i.e., AFM, ferromagnetic (FM), and a phase with random or oscillatory behavior (R). The phase transitions are observed between FM and R phases when for all ${\mathrm{\Delta }}_{\mu }\ne 0.0$, between FM and AFM when ${\mathrm{\Delta }}_{\mu }=0.0$ only and, AFM and R at low temperatures for very small ${\mathrm{\Delta }}_{\mu }$ and $H_{\mu }$ values.

The mean-field expressions derived from the transverse Ising model are used to investigate the second-order ferroelectric phase transition. With this theory, the properties of ferroelectric thin films formed by inserting a monolayer of material B into material A in the middle was studied. Firstly, a recursive equation for the phase transition properties of the ferroelectric thin film with one distinct inserting-layer in the middle was obtained. Next, the effect of the exchange interaction and transverse field parameters of materials A and B on the phase diagrams was investigated. The results show that with the modification of the parameter values of the inserting-layer B, the properties of the phase transition, the crossover value of the transverse field, the polarizations of different layers, and the critical temperature, change sensitively.

First-principles calculations within density functional theory (DFT) with the projector augmented wave (PAW) technique were used to investigate the stabilities of intermetallics in the Au–Rb system at 0 K. Four intermetallics: Au₇Rb₃, Au₃Rb₂, Au₅Rb and AuRb were investigated in their observed experimental structures. The Au₂Rb compound, reported in the Au–Rb phase diagrams without specifying explicitly its structure, was also investigated by inspecting several hypothetical structures. A suspect compound (AuRb₂) was also investigated. Results show that: (i) The Au₃Rb₂ and Au₇Rb₃ compounds, which were never reported in any Au–Rb phase diagram, are stable at 0 K. (ii) The Au₂Rb compound is not a ground state for all the tested structures. (iii) Stability of the Au₅Rb and AuRb compounds was confirmed. (iv) The new compound AuRb₂, not yet reported experimentally, is found mechanically stable at 0 K.

The solid solutions of ${\mathrm{\text{Ca}}}_x{\mathrm{\text{Ba}}}_{1-x}{\mathrm{\text{Ga}}}_2{\mathrm{\text{S}}}_4(x=0,0.1,\dots ,1)$ were synthesized by solid-phase reactions from powder components of CaS, BaS, and Ga₂S₃. The temperature-concentration dependences of the Gibbs free energy of formation of ${({\mathrm{\text{CaGa}}}_2{\mathrm{\text{S}}}_4)}_x{({\mathrm{\text{BaGa}}}_2{\mathrm{\text{S}}}_4)}_{1-x}$ solid solutions from ternary compounds and phase diagrams of the CaGa₂S₄–BaGa₂S₄ were determined by a calculation method. It was revealed that continuous solid solutions are formed in these systems. The spinodal decomposition of ${({\mathrm{\text{CaGa}}}_2{\mathrm{\text{S}}}_4)}_x{({\mathrm{\text{BaGa}}}_2{\mathrm{\text{S}}}_4)}_{1-x}$ solid solutions into two phases is predicted at ordinary temperatures.

This work presents a study of the magnetic and magnetocaloric properties of mixed spins ($\sigma =1$, $S=3/2$) in a Graphullerene-like nanostructure. Monte Carlo simulations (MCs) were conducted using the Metropolis algorithm in the Blume–Capel model. The ground state phase diagrams were established and illustrated for different physical parameters. Additionally, the corresponding magnetizations, susceptibilities, specific heat, Binder cumulant, magnetic and change entropies were examined versus temperature. The critical temperature was determined, and hysteresis cycles were presented for specific physical parameter values. The results suggest that the structure shows potential as a candidate for magnetic refrigeration.

The antiferromagnetic (AFM) spin-3/2 Heisenberg model is explored by using a mean-field approach (MFA) with the inclusion of spin operators for a square lattice. The considered Hamiltonian consists of the bilinear exchange interaction $J_z$ and Dzyaloshinskii–Moriya interaction (DMI) ${\mathrm{\Delta }}_m$ parameters between the nearest-neighbor (NN) spins along the z- and y-axes and external magnetic field components $H_x$ and $H_z$ acting along the x- and z-axes, respectively. After obtaining the mathematical formulation of the magnetization components along the x- and z-directions in the MFA, their thermal changes are inspected to obtain the phase diagrams on the (${\mathrm{\Delta }}_m$, T) and (H, T) planes for the given values of $H=H_x=H_z$ and ${\mathrm{\Delta }}_m$, respectively, with $J_z=-1$ which leads to AFM interactions. It is found that the model not only presents the AFM and ferromagnetic (FM) phases but also the random (R) phase regions created by the existence of ${\mathrm{\Delta }}_m$ interaction. These three phases are observed to coexist for the appropriate values of given system parameters. The phase lines exhibit reentrant behavior when only the FM and R phases are present.