scholarly journals The Monte Carlo simulation of 2D ANNNI-model

2018 ◽  
Vol 185 ◽  
pp. 11010
Author(s):  
Murtazaev Akai Kurbanovich ◽  
Ibaev Zhavrail Gadzhievich
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Interaction Parameter ◽  
Nearest Neighbor ◽  
Wave Number ◽  
Transition Temperatures ◽  
Annni Model ◽  
Absolute Value ◽  
Temperature Dependences ◽  
Competing Interaction

In this, study we present the data for 2D Axial Next Nearest Neighbor Ising model (ANNNI-model) obtained from Monte Carlo (MC) simulations using the standard Metropolis algorithm. The temperature dependences of thermodynamic parameters for a cubic lattice with linear sizes L=32 at different values of the competing interaction parameter |J1/J|=0.1÷1.0. Transition temperatures of ferromagnetic ordering to the paramagnetic state at |J1/J|<0.3 and to the modulated state at 0.3<|J1/J|<0.5 are shown to shift towards low temperatures with an increase in a competing interaction parameter absolute value. Conversely, transition temperatures of the modulate state to the paramagnetic ordering grow. The modulated ordering in the 2D ANNNImodel appears in the temperature range 0.1<T<2.0 at 0.2<|J1/J|≤1.0. Modulated structure parameters are computed using a mathematic apparatus of Fourier transform spectral analysis. According to the Fourier analysis results, the wave number grows with an increase in the competing interaction parameter absolute value. Summarizing obtained results, we plot a phase diagram of 2D anisotropic Ising model with competing interactions.

Monte Carlo simulations of long-range order kinetics in B2 phases

1995 ◽  
Vol 10 (3) ◽  
pp. 591-595 ◽  
Author(s):  
K. Yaldram ◽  
V. Pierron-Bohnes ◽  
M.C. Cadeville ◽  
M.A. Khan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Nearest Neighbor ◽  
Vacancy Concentration ◽  
Relaxation Times ◽  
Nearest Neighbors ◽  
Migration Energy ◽  
Ordering Kinetics ◽  
Migration Barriers ◽  
Temperature Dependences

The thermodynamic parameters that drive the atomic migration in B2 alloys are studied using Monte-Carlo simulations. The model is based on a vacancy jump mechanism between nearest neighbor sites, with a constant vacancy concentration. The ordering energy is described through an Ising Hamiltonian with interaction potentials between first and second nearest neighbors. Different migration barriers are introduced fur A and B atoms. The results of the simulations compare very well with those of experiments. The ordering kinetics are well described by exponential-like behaviors with two relaxation times whose temperature dependences are Arrhenius laws yielding effective migration energies. The ordering energy contributes significantly to the total migration energy.

A Monte Carlo and renormalization group study of the Ising model with nearest and next nearest neighbor interactions on the triangular lattice

1983 ◽  
Vol 61 (11) ◽  
pp. 1515-1527 ◽  
Author(s):  
James Glosli ◽  
Michael Plischke
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Ising Model ◽  
Potts Model ◽  
Triangular Lattice ◽  
Nearest Neighbor ◽  
Universality Class ◽  
Energy Functional ◽  
First Order ◽  
Universality Classes

The Ising model with nearest and next nearest neighbor antiferromagnetic interactions on the triangular lattice displays, for Jnnn/Jnn = 0.1, three phase transitions in different universality classes as the magnetic field is increased. We have studied this model using Monte Carlo and renormalization group techniques. The transition from the paramagnetic to the 2 × 1 phase (universality class of the Heisenberg model with cubic anisotropy) is found to be first order; the transition from the paramagnetic phase to the [Formula: see text] phase (universality class of the three state Potts model) is continuous; and the transition from the paramagnetic to the 2 × 2 phase (universality class of the four state Potts model) is found to change from first order to continuous as the field is increased. We have mapped out the phase diagram and determined the critical exponents for the continuous transitions. A novel technique, using a Landau-like free energy functional determined from Monte Carlo calculations, to distinguish between first order and continuous transitions, is described.

scholarly journals 3D ISING NONUNIVERSALITY: A MONTE CARLO STUDY

2005 ◽  
Vol 16 (08) ◽  
pp. 1217-1224 ◽  
Author(s):  
MELANIE SCHULTE ◽  
CAROLINE DROPE
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
External Field ◽  
Nearest Neighbor ◽  
Monte Carlo Study ◽  
Universality Class ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Binder Cumulant

We investigate as a member of the Ising universality class the Next-Nearest Neighbor Ising model without external field on a simple cubic lattice by using the Monte Carlo Metropolis Algorithm. The Binder cumulant and the susceptibility ratio, which should be universal quantities at the critical point, were shown to vary for small negative next-nearest neighbor interactions.

scholarly journals Термодинамические и магнитные свойства двумерной анизотропной модели Изинга с конкурирующими взаимодействиями

2019 ◽  
Vol 61 (10) ◽  
pp. 1911
Author(s):  
А.К. Муртазаев ◽  
Ж.Г. Ибаев
Keyword(s):  
Exchange Interactions ◽  
Square Lattice ◽  
Wave Number ◽  
Two Dimensional ◽  
Competing Interactions ◽  
Distinctive Features ◽  
Magnetic Parameters ◽  
Modulated Structures ◽  
Temperature Dependences ◽  
Competing Interaction

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

SPIN ◽  
2018 ◽  
Vol 08 (03) ◽  
pp. 1850010
Author(s):  
D. Farsal ◽  
M. Badia ◽  
M. Bennai
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Phase Diagram ◽  
Monte Carlo ◽  
Magnetic Susceptibility ◽  
Critical Temperature ◽  
Ising Model ◽  
Nearest Neighbor ◽  
Two Dimensional ◽  
The 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.

Investigation of the 3D ANNNI Model by Monte Carlo Methods

2009 ◽  
Vol 152-153 ◽  
pp. 575-578 ◽  
Author(s):  
Akai K. Murtazaev ◽  
J.G. Ibaev ◽  
Ya.K. Abuev
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Ising Model ◽  
Temperature Dependence ◽  
Monte Carlo Methods ◽  
Thermal Parameters ◽  
Competing Interactions ◽  
Annni Model

The results for 3D anisotropic Ising model with competing interactions (ANNNI) investigated by the Monte Carlo methods are presented. The temperature dependence of thermal parameters is calculated. The character of all possible phase transitions in the model is analyzed.

scholarly journals Investigation of Multicritical Phenomena in ANNNI Model by Monte Carlo Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-4
Author(s):  
A. K. Murtazaev ◽  
J. G. Ibaev
Keyword(s):  
Phase Diagram ◽  
Heat Capacity ◽  
Monte Carlo ◽  
Ising Model ◽  
Wide Temperature Range ◽  
Monte Carlo Methods ◽  
Correlation Radius ◽  
Competing Interactions ◽  
Annni Model ◽  
Lifshitz Point

The anisotropic Ising model with competing interactions is investigated in wide temperature range and |J1/J| parameters by means of Monte Carlo methods. Static critical exponents of the magnetization, susceptibility, heat capacity, and correlation radius are calculated in the neighborhood of Lifshitz point. According to obtained results, a phase diagram is plotted, the coordinates of Lifshitz point are defined, and a character of multicritical behavior of the system is detected.

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