Two-dimensional Anisotropic Ising Model Research Articles

Thermodynamic Properties and Magnetocaloric Effect of Spins - 1/2 Square Lattice

This work aims to investigate the thermodynamic properties and magnetocaloric effect (MCE) of spins - 1/2 square lattice using Monte Carlo simulation. The considered Ising model is parameterized by the couplings J, [Formula: see text] and [Formula: see text]; where J is the ferromagnetic exchange interaction between first nearest-neighbor spins, a is the anisotropic parameter and [Formula: see text] is the ferromagnetic exchange interaction between second nearest-neighbor spins. Monte Carlo simulation under Metropolis algorithm allows us to study some thermodynamic properties and MCE of spins - 1/2 square lattice. The discussion of the obtained results allowed us to specify the conditions which can enrich the MCE in spins - 1/2 square lattice. The two-dimensional anisotropic Ising model presents clarifying the critical point of the ferromagnetic–paramagnetic transition, and we have shown that the maximum entropy variation increases when it occurs at the ferromagnetic–paramagnetic transition temperature regardless of the intensity of the applied magnetic field and the values of “a” and “b”.

Study of the Two-Dimensional Anisotropic Ising Model with Competing Interactions in the Region of a Transition from the Ferromagnetic to Paramagnetic State

The two-dimensional anisotropic Ising model with competing interactions in the region of a transition from the ferromagnetic to paramagnetic phase has been studied by the Monte Carlo method using the Wang–Landau algorithm. State density distributions have been obtained and the order parameters corresponding to different energies have been calculated. The temperature dependences of the thermodynamic parameters including the internal energy, magnetization, free energy, entropy, specific heat at constant magnetization, and Binder cumulants have been calculated. Using the Binder cumulant method and histogram analysis, it has been shown that a single second-order phase transition from the ferromagnetic to paramagnetic phase occurs at two exchange coupling constants ratios |J1/J| = 0.1 and 0.2 in the two-dimensional anisotropic next-nearest neighbor Ising model. The phase transition temperatures have been calculated. The main critical exponents have been determined using the finite-size scaling theory.

Thermodynamic and Magnetic Properties of the Two-Dimensional Anisotropic Ising Model with Competing Interactions

The two-dimensional anisotropic Ising model with competing interactions is studied on a square lattice by Monte Carlo methods using the Wang–Landau algorithm. The temperature dependences of the main thermodynamic and magnetic parameters are calculated. The distinctive features of temperature dependences of these parameters for different values of the competing interaction are shown. The dependences of the wave number of modulated structures on the ratio of exchange interaction parameters are plotted. The phase diagram of the model is built. The coordinates of the Lifshits point and the localization region of the phases with different wave vector values are calculated by interpolating phase boundaries of the d-iagram.

Monte Carlo Calculations of the Density of States for a Two-Dimensional Anisotropic Ising Model with Competing Interactions

A two-dimensional anisotropic Ising model with competing interactions on a square lattice is investigated using the Monte Carlo approach, based on the Wang–Landau algorithm. The curves of the density-of-states distribution and the order parameter are obtained. It is shown that the density-of-states distribution jumps sharply when |J1/J| = 0.6, due to strong degeneration of the modulated state. Sharp jumps are also observed on the distributions of the order parameter when |J1/J| > 0.2, testifying to the system’s transition from a homogeneous ordered state to a modulated phase.

Термодинамические и магнитные свойства двумерной анизотропной модели Изинга с конкурирующими взаимодействиями

The two-dimensional anisotropic Ising model was studied with competing interactions on a square lattice using Monte-Carlo methods using the Wang-Landau algorithm. The temperature dependences of the main thermodynamic and magnetic parameters are calculated. The distinctive features of the temperature dependences of these parameters are shown for different values of the competing interaction. The graphs of the dependence of the wave number of modulated structures on the ratio of the parameters of exchange interactions are plotted. Built phase diagram of the model. Interpolating the phase boundaries of the diagram, the coordinates of the Lifshchits point and phase localization areas with different wave vector values are calculated.

Phase Transition in 2D Anisotropic Ising Model with Next-Nearest Neighbor Interactions in a Magnetic Field

The critical behavior at the phase transition of the ferromagnetic two-dimensional anisotropic Ising model with next-nearest neighbor (NNN) couplings in the presence of the field is determined using mainly Monte Carlo (MC) method. This method is used to investigate the phase diagram of the model and to verify the existence of a divergence at null temperature which often appears in two-dimensional systems. We analyze also the influence of the report of the NNN interactions [Formula: see text] and the magnetic field [Formula: see text] on the critical temperature of the system, and we show that the critical temperature depends on the magnetic field for positive values of the interaction. Finally, we have investigated other thermodynamical qualities such as the magnetic susceptibility [Formula: see text]. It has been shown that their thermal behavior depends qualitatively and quantitatively on the strength of NNN interactions and the magnetic field.

Modeling of the financial market using the two-dimensional anisotropic Ising model

We have used the two-dimensional classical anisotropic Ising model in an external field and with an ion single anisotropy term as a mathematical model for the price dynamics of the financial market. The model presented allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets. We have obtained the mean price in terms of the strong of the site anisotropy term Δ which reinforces the sensitivity of the agent’s sentiment to external news.

Critical Properties of Two-dimensional Anisotropic Ising Model on a Square Lattice

We study the critical behavior of two-dimensional anisotropic Ising model on a square lattice by the finite cluster approximation based on a single-site cluster theory and by Monte Carlo techniques. We analize the influence of the report of the interactions J h /J v on the critical temperature of the system, and we show that the critical exponents depend only on the very general properties of the systems and not on the detail of the interactions. Finally, we do a comparison between the finite cluster approximation, the mean-field approximation, and the Monte Carlo method on the level of the phase diagram in the plan $\left (J_{h}/T_{c}\text { },\text { } J_{v}/T_{c}\right ).$

Critical Binder cumulant in a two-dimensional anisotropic Ising model with competing interactions

The Binder cumulant at the phase transition of Ising models on square lattices with ferromagnetic couplings between nearest neighbors and with competing antiferromagnetic couplings between next-nearest neighbors, along only one diagonal, is determined using Monte Carlo techniques. In the phase diagram a disorder line occurs separating regions with monotonically decaying and with oscillatory spin-spin correlations. Findings on the variation of the critical cumulant with the ratio of the two interaction strengths are compared to related recent results based on renormalization-group calculations.

Detwinning mechanism, twinning dislocations and planar defects in YBa 2Cu 3O 7−δ

The detailed geometry of twin boundaries in YBa 2Cu 3O 7− δ is discussed on the basis of high-resolution electron microscopy observations. “Sharp” as well as “diffuse” twin boundaries are observed, depending on the composition and thermal history of the sample. It is shown by means of Monte Carlo simulations based on a two-dimensional anisotropic Ising model that the concentration of oxygen ions in the CuO 1−δ layers exhibits a minimum in the region adjacent to the twin interface. The vacancy enriched region is more pronounced at low temperature and disappears at high temperature. A model is proposed for twinning dislocations in YBa 2Cu 3O 7−δ and it is shown that the ordering stresses created by the tetragonal-orthorhombic phase transition induce the “synchro-shear” motion of such twinning dislocations, leading to the lateral displacement of twin interfaces. It is shown that this atomic model for twinning dislocations provides an atomic mechanism for the “detwinning” of crystals under uniaxial compression. Crystallographic shear planes accommodating an excess of CuO are observed; Frank dislocations bordering such shear planes have been analysed as well.

Monte Carlo simulation of oxygen ordering in YBa 2 Cu 3 O z .

Abstract Oxygen ordering in the basal plane of YBa2Cu3Oz has been studied by Monte Carlo simulations of a two-dimensional anisotropic Ising model. The orthorhombic to tetragonal transition is found to be second order at high temperature in agreement with previous CVM calculations. At low temperatures, a cell-doubled orthorhombic phase appears near stoichometry z=6.5, intermediate between the single cell orthorhombic and tetragonal phases. At very low temperatures, long-lived transient O Cu O chain ordering is observed to lead to triple and fivefold unit cells. Where not obscured by transient ordering, the transition lines bordering the orthorhombic cell-doubled phase are found to be second order. The observed equilibrium and non-equilibrium structures correlate well with atomic resolution micrographs and diffraction data from the YBa2Cu3Oz system.

Monte Carlo study of transient states of order in YBa2Cu3Oz.

Monte Carlo simulations of oxygen ordering in the YBa{sub 2}Cu{sub 3}O{sub {ital z}} system have been performed using a two-dimensional anisotropic Ising model. In agreement with experimental findings, transient phases are obtained at low temperatures. Observed structures are investigated, and the kinetics of their domain formation is described. The convergence of the system is seen to be exceptionally slow, and the rate of domain evolution is found to increase with decreasing oxygen content. The implications of these findings on the development of a complete theoretical ordering model for this system are discussed.