Papers by Keyword: Ising Model

Abstract: Ising core-shell model was proposed to reconstruct superparamagnetism hysteresis in nano-goethite (α-FeOOH). Core and shell set as antiferromagnetic and paramagnetic state respectively. Core and shell radius varies until the theoretical hysteresis fit with experiment hysteresis. At low temperature, the hysteresis reconstructed nicely with 55% antiferromagnetic core contribution and 45% paramagnetic shell contribution. At high temperature, the core-shell model show unrealistic result compared to the pure paramagnetic state.

Abstract: We considered the Ising 1D chain in an external magnetic field taking into account the nearest and next-nearest interactions. By the method of Kramers–Wannier transfer-matrix, the rigorous analytical expression for Fourier-transform of pair spin-spin correlation function was obtained, and the temperature evolution of the scattering was analyzed for various relations of exchange parameters.

Abstract: We studied magnetic orderings and frustrations on 1D chain and 2D lattices: square, triangular, kagome, and hexagonal in the Ising, 3-state Potts and standard 4-state Potts models. The spins interrelate with one another via the nearest-neighbor, the next-nearest-neighbor or the third-neighbor exchange interactions and by an external magnetic field. For problem solving we mainly calculated the entropy and specific heat using the rigorous analytical solutions for maximum eigenvalue of Kramers-Wannier transfer-matrix and exploiting computer simulation, par excellence, by Wang-Landau algorithm. Whether a system is ordered or frustrated is related to the signs and values of exchange interactions. An external magnetic field may both favor the ordering of a system and create frustrations. With the help of calculations of the entropy, the specific heat and magnetic parameters, we obtained the points and ranges of frustrations, the frustration fields and the phase transition points. The results obtained also show that the same exchange interactions my either be competing or noncompeting which depends on the topology of a lattice.

Abstract: 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.

Abstract: In this paper, we investigated the magnetocaloric effect (MCE) in one-dimensional magnets with different types of ordering in the Ising model, Heisenberg, XY-model, the standard, planar, and modified Potts models. Exact analytical solutions to MCE as functions of exchange parameters, temperature, values and directions of an external magnetic field are obtained. The temperature and magnetic field dependences of MCE in the presence of frustrations in the system in a magnetic field are numerically computed in detail.

Abstract: The phase transitions in antiferromagnetic Ising model are studied on a body-centered cubic lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transitions of second order. A static magnetic critical indices is calculated using the finite-dimensional scaling theory.

Abstract: Simulating Ising model to calculate magnetization intensity by Monte Carlo method. The Ising model was introduced simply, sampled importantly, and calculated with programming. It shows the dependency relationship between the magnetization intensity and the size of dot-square line in different temperatures for Ising model. It cans edulcorate the approximation of analytic method by computer simulating. It obtains a method to appraise a model right or wrong by comparing the model and the experimental data.

Abstract: The critical properties of two-dimensional antiferromagnetic Ising model in square lattice are investigated using the replica Monte-Carlo method with account of interactions of second nearest neighbors. The diagram of critical temperature dependence on an interaction value of second nearest neighbors is plotted. Static critical exponents of the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated for this model using the finite-size scaling theory.

Abstract: This work investigated properties of diffusive magnetic particles. Random walk Monte Carlo method was used to simulate the Ising spin diffusing and flipping to examine the properties of the system. The Ising spins interact among themselves via Lennard-Jones interaction. Metropolis algorithm was employed to update spins configuration on the continuous space. The volume of Ising spins, magnetization and magnetic susceptibility, were investigated as functions of temperature, number of Ising spins in the system and simulation time. It was found that, at low temperatures, the Ising spins tend to stay close even at long simulation time, where finite magnetization was found suggesting the ferromagnetic preference. However, at high temperatures, paramagnetic behavior reveals as ferromagnetic interaction ceases with time passing. This is due to role of spin diffusing which causes the spins to disperse and hence ferromagnetic interaction among spins reduces.

Abstract: This work investigated the competition effect between the ferro-and antiferro-interaction on the domain size and domain interface in two-dimensional binary alloy. Monte Carlo simulation and Ising model were used to model the alloy system where largest domain size and the domain interface were observed to identify the low temperature ordered phase and the high temperature disordered phase. The simulation results show that domain size is maximized when the ferro-interaction is preferred, but domain interface becomes maximum instead when the antiferro-interaction is favored. These domain properties were reported as a function of temperature for various magnitude of ferro-and antiferro-interactions. In addition, the artificial neural network was used to create database of relationship among the ferro-and antiferro-interaction, the simulated temperature and the domain properties. Good agreement between the real targeted outputs and the predicted outputs was found, which confirm the learning-by-example ability of the artificial neural network. This work therefore presents another step in the understanding of how complex interaction plays its role in binary alloy problem and how a data mining technique assists development of understanding in materials science problems.