Topological defects and magnetization processes for the triangular lattice of ising particles with an antiferromagnetic interaction

JETP Letters - For the frustrated triangular lattice of Ising magnetic moments with an antiferromagnetic interaction, which is in a state with two sublattices, a new type of topological defects...     

The density of states for an antiferromagnetic Ising model on a triangular lattice

The Wang-Landau algorithm is an efficient Monte Carlo approach to the density of states of a statistical mechanics system. The estimation of state density would allow the computation of thermodynamic properties of the system over the whole temperature range. We apply this sampling method to study the phase transitions in a triangular Ising model. The entropy of the lattice at zero temperature as well as other thermodynamic properties is computed. The calculated thermodynamic properties are explained in the context of the magnetic phase transition.      

Incommensurate-commensurate phase transitions in an anisotropic antiferromagnetic model on triangular lattice

An anisotropic antiferromagnetic model on a triangular lattice with competing interactions is investigated by the cluster transfer-matrix method. A phase diagram with ferrimagnetic, incommensurate, and disordered phases is found. Three order parameters are introduced. At commensurate-incommensurate and incommensurate-disorder phase transition lines two of them change in continuous and one in discontinuous way.     

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 two-dimensional antiferromagnetic Potts model on a triangular lattice

Phase transitions and thermodynamic properties in the two-dimensional three-state antiferromagnetic Potts model on a triangular lattice are investigated using the Monte Carlo method and the histogram analysis of the data. It is shown that pronounced first-order phase transitions are observed in this model for systems with rather large linear dimensions (L > 120). No first-order PTs are observed for systems with L < 120.     

Phase transitions in the two-dimensional ferro- and antiferromagnetic potts models on a triangular lattice

The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20–120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory.     

Diffusion of particles over triangular inhomogeneous lattice with two non-equivalent sites

We investigate the diffusion of particles adsorbed on a triangular lattice with deep and shallow sites. It is shown that the character of the particle migration depends substantially on the relative jump rates from the deep and shallow sites. The site inhomogeneity imposes specific correlation betweeen successive jumps: particles perform pairs of slow and fast jumps. General analytical expressions have been derived for the chemical and jump diffusion coefficients. We have calculated coverage dependencies of the diffusion coefficients and some thermodynamic quantities for different lateral interactions between the particles. The analytical data have been compared with the numerical data obtained by kinetic Monte Carlo simulations. The agreement between the results obtained by these quite different approaches is found to be very satisfactory.     

Simulation of magnetization reversal processes in finite ferromagnets with defects

The magnetization and magnetization reversal processes that occur through the mechanism of incoherent rotation of magnetic moments in cubic ferromagnets with limited sizes are investigated theoretically. It is established that the appropriate model representation of magnetic inhomogeneities arising in the region of defects is provided by 0° domain walls. The influence of the external magnetic field on the structure and the stability region of the 0° domain walls is determined. This makes it possible to reveal the characteristic features of the magnetization reversal of real crystals as a function of the material and defect parameters, in particular, in the vicinity of the spin-reorientation phase transition.     

Study of critical properties of the frustrated antiferromagnetic Heisenberg model on a triangular lattice

The replica Monte Carlo method has been applied to study critical properties of the three-dimensional frustrated antiferromagnetic Heisenberg model on a layered triangular lattice. Magnetic and chiral critical exponents for this model have been calculated within the finite-size scaling theory. The data for this model have been analyzed for the first time taking into account corrections to scaling. It has been shown that the critical behavior of the frustrated antiferromagnetic Heisenberg model on the triangular lattice differs from the critical behavior of the pure Heisenberg model and is independent of the type of interlayer exchange interaction.     

Phase transitions in the antiferromagnetic Heisenberg model on a layered triangular lattice with the next-nearest neighbor interactions

Phase transitions in the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with the next-nearest neighbor interactions have been studied by the histogram Monte Carlo method. Phase transitions in this model have been studied in the range of the next-nearest neighbor interactions from 0.0 to 1.0. The first-order phase transition has been revealed in the considered interval in the studied model.     

Critical temperatures of triangular Ising lattice with small second neighbor interaction

The next-nearest neighbor correlation function for isotropic triangular Ising system has been evaluated. This function is used to determine the shifts in the critical temperatures of ferromagnetic and antiferromagnetic triangular lattice after introduction of a small next-nearest neighbor interaction in zero field.     

Critical behavior and spatial crossover in the frustrated antiferromagnetic Heisenberg model on a triangular lattice

The critical properties of the three-dimensional frustrated Heisenberg model on a layered triangular lattice with variable interplane exchange interaction have been investigated by the replica Monte Carlo method. All main magnetic and chiral critical exponents have been calculated. It is found that a decrease in the interlayer exchange leads to crossover from the three-to two-dimensional critical behavior.     

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.     

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.     

On the magnetization process in an ising-spin lattice

Gamma ray spectra of a mixture of the isotopes⁸⁶Br and⁸⁷Br have been measured by means of a Ge(Li) detector. Both manual and automated techniques were used to separate bromine from other fission products of natural uranium. A total of 13 gamma rays were observed. The most intense of the⁸⁶Br gamma peaks (1,565 keV) was found to grow in with a half-life of 4.5±1 s. This is explained to be due to an isomeric state in⁸⁶Br decaying to the ground state.     

Phase transition of the compressible ising lattice

It is shown that the presence of harmonic lattice vibrations in a spin-$\text{1}\text{2}$ Ising system leads, in the mean field approximation, to transitions of first or second order, according to whether the pressure lies below or above a critical value. The results are being discussed in relation to experiments on the order-disorder transition in NH₄Cl.