F. A. Kassan-Ogly

Ising model on a square lattice with second-neighbor and third-neighbor interactions

We studied the phase transitions and magnetic properties of the Ising model on a square lattice by the replica Monte Carlo method and by the method of transfer-matrix, the maximum eigenvalue of which was found by Lanczos method. The competing exchange interactions between nearest neighbors J1, second J2, third neighbors J3 and an external magnetic field were taken into account. We found the frustration points and expressions for the frustration fields, at crossing of which cardinal changes of magnetic structures (translational invariance changes discontinuously) take place. A comparative analysis with 1D Ising model was performed and it was shown that the behavior of magnetic properties of the 1D model and the 2D model with J1 and J3 interactions reveals detailed similarity only distinguishing in scales of magnetic field and temperature.

Phase transitions in the antiferromagnetic ising model on a square lattice with next-nearest-neighbor interactions

The phase transitions in the two-dimensional Ising model on a square lattice are studied using a replica algorithm, the Monte Carlo method, and histogram analysis with allowance for the next-nearest-neighbor interactions in the range 0.1 ≤ r < 1.0. A phase diagram is constructed for the dependence of the critical temperature on the next-nearest-neighbor interaction. A second-order phase transition is detected in this range and the model under study.

Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice with interactions between next-to-nearest neighbors

Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice are studied on the basis of the replica algorithm by the Monte Carlo method and histogram analysis taking into account the interaction of next-to-nearest neighbors. The phase diagram of the dependence of the critical temperature on the intensity of interaction of the next-to-nearest neighbors is constructed. It is found that a second-order phase transition is realized in this model in the investigated interval of the intensities of interaction of next-to-nearest neighbors.

Frustrations and phase transitions in the three-vertex Potts model with next-nearest-neighbor interactions on a triangular lattice

Phase transitions in two-dimensional arrays described by the three-vertex Potts model involving the interactions between magnetic moments located at the nearest-neighbor and next-nearest-neighbor sites of a triangular lattice are studied using the Monte Carlo method. The ratio of the next-nearest-neighbor and nearest-neighbor exchange constants r = J2/J1 is chosen within the 0–1 range. The analysis of the low temperature behavior of the entropy and density of states in the system, as well as of the fourth-order Binder cumulants, shows that in the range 0 ≤ r < 0.2, this model exhibits a first-order phase transition, whereas at r ≥ 0.2, frustrations arise in such a system.

Dynamical rearrangement of domain walls with vortex internal structure in magnetic uniaxial films with in-plane anisotropy.

New mechanisms of dynamic rearrangement of internal vortex structure of moving domain walls (topological solitons with internal degrees of freedom) in magnetic uniaxial film with an easy axis in its plane are revealed. A nonlinear dependence of the bifurcation field, above which a wall motion become nonstationary, is found on the film thickness, the magnetization saturation, and the anisotropy field.

Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J1 and J2, respectively. PTs in these models are analyzed for the ratio r = J2/J1 of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J1 < 0 and J2 < 0 exhibits a first-order PT in the range of 0 ⩽ r < 0.2, whereas, in the interval 0.2 ⩽ r ⩽ 1.0, frustrations arise in the system. At the same time, for J1 > 0 and J2 < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ⩽ |r| ⩽ 1/3, the model exhibits a second-order PT.

Structure and dynamic properties of asymmetric vortexlike domain walls in inhomogeneous magnetic films with an in-plane anisotropy: I. Equilibrium structures. Nonlinear dynamics in two-layered films

Within the framework of a two-dimensional distribution of magnetization and exact allowance for the basic interactions, including dipole-dipole one, the static properties and nonlinear dynamic behavior of vortexlike domain walls in multilayer magnetically uniaxial films with an in-plane anisotropy have been studied. It has been shown that in such films, just as in single-layer ones, there exist asymmetric vortexlike walls; however, in this case the wall vortices prove to be moved toward the layers with a higher magnetization or toward the layers with a lower anisotropy. At some thicknesses of the layers and magnetization differences in them, the asymmetric Néel walls prove to be unstable. New scenarios of the dynamic transformation of the structure of the walls in multilayer films have been established, which in some cases differ significantly from the appropriate scenarios in the single-layer films.

Static properties of asymmetric vortex-like domain walls in magnetically uniaxial thick films

The structure and energy of asymmetric vortex-like Bloch and Néel walls in a magnetically uniaxial film with an easy magnetization axis lying in the film plane are investigated by numerically minimizing the total energy within the rigorous micromagnetic approach and the two-dimensional model of the magnetization distribution. The calculations are performed over wide ranges of film thicknesses b (up to b = 1 μm) and magnetic parameters of the films. It is established that the asymmetric vortex-like domain walls are the most universal wall structures in the films under consideration. In magnetically uniaxial films, unlike in magnetically multiaxial films, the asymmetric Bloch walls are always stable.

Phase transitions in crystals with a BCC structure

A theory of bcc-hcp and bcc-fcc structural phase transformations in metals with a high-temperature bcc lattice has been constructed on the basis of a pseudo-spin Ising Hamiltonian, which describes cooperative oscillations of atomic planes in a two-well potential with allowance for interactions between nearest neighbors. The picture of diffuse scattering and of the combined rearrangement of original Bragg reflections and diffuse scattering into Bragg reflections upon transitions into low-temperature phases has been calculated at all temperatures. It is shown that the bcc-hcp and bcc-fcc phase transformations occur in a temperature interval rather than at a point. In the case of the bcc-hcp transformation, as the temperature decreases, the bcc structure first transforms jumpwise into an orthorhombic structure close to the hcp structure and then, with a further decrease in temperature, this structure smoothly changes into the strictly close-packed hexagonal structure at T → 0. In the case of the bcc-fcc transition, there occurs an analogous transformation into a strictly close-packed face-centered cubic structure at T → 0, but now through a monoclinic structure.

Exact Solution of 1D Ising Model on Linear Chain with Arbitrary Spin

We investigated the Ising model on a linear chain with arbitrary spin including interactions between nearest and next-nearest neighbors in an applied magnetic field. A series of exact solutions and formulas for frustration fields, magnetizations and entropies at these fields at T→0 are found.