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.

scholarly journals Low-temperature antiferromagnetism of Ising model with competing interactions

2021 ◽  
pp. 64-71
Author(s):  
Kirill Tsiberkin ◽  
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Temperature Shift ◽  
Second Order ◽  
Square Lattice ◽  
Antiferromagnetic Coupling ◽  
Competing Interactions ◽  
Saturation State ◽  
Spin Configuration ◽  
Competing Interaction

The paper presents a numerical analysis of equilibrium state and spin configuration of square lattice Ising model with competing interaction. The most detailed description is given for case of ferromagnetic interaction of the first-order neighbours and antiferromagnetic coupling of the second-order neighbours. The numerical method is based on Metropolis algorithm. It uses 128×128 lattice with periodic boundary conditions. At first, the simulation results show that the system is in saturation state at low temperatures, and it turns into paramagnetic state at the Curie point. The competing second-order interaction makes possible the domain structure realization. This state is metastable, because its energy is higher than saturation energy. The domains are small at low temperature, and their size increases when temperature is growing until the single domain occupies the whole simulation area. In addition, the antiferromagnetic coupling of the second-order neighbours reduces the Curie temperature of the system. If it is large enough, the lattice has no saturation state. It turns directly from the domain state into paramagnetic phase. There are no extra phases when the system is antiferromagnetic in main order, and only the Neel temperature shift realizes here.

THE HELIX-COIL TRANSITION IN A DOUBLE-STRANDED POLYNUCLEOTIDE AND THE TWO-DIMENSIONAL RANDOM WALK

2012 ◽  
Vol 26 (13) ◽  
pp. 1250083
Author(s):  
G. N. HAYRAPETYAN ◽  
V. F. MOROZOV ◽  
V. V. PAPOYAN ◽  
S. S. POGHOSYAN ◽  
V. B. PRIEZZHEV
Keyword(s):  
Random Walk ◽  
Hydrogen Bonds ◽  
Polymer Chains ◽  
Square Lattice ◽  
Two Dimensional ◽  
Competing Interactions ◽  
New Approach ◽  
Rich Phase ◽  
Coil Transition ◽  
The Rich

The helix-coil transition in a double-stranded homopolynucleotide is considered. The new approach to the melted loops account is proposed. The relative distance between the corresponding monomers of two polymer chains is modeled by the two-dimensional random walk on the square lattice. Returns of the random walk to the origin describe the formation of hydrogen bonds between complementary units. To take into account the interaction of monomers inside the chains, we consider various regimes of return to the origin. One of them involves two competing interactions and demonstrates a nontrivial sharp denaturation transition. The rich phase behavior of the double-stranded homopolynucleotide is discussed in terms of the proposed approach.

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.

Influence of the Surface on the Thermodynamic and Magnetic Properties of the Anisotropic Ising Model with Competing Interactions

2016 ◽  
Vol 845 ◽  
pp. 97-100
Author(s):  
Akai K. Murtazaev ◽  
Zhavrail G. Ibaev
Keyword(s):  
Monte Carlo ◽  
Magnetic Properties ◽  
Ising Model ◽  
Thermodynamic Properties ◽  
Thermodynamic Parameters ◽  
Monte Carlo Methods ◽  
Magnetic Ordering ◽  
Competing Interactions ◽  
Modulated Structures ◽  
Temperature Dependences

The thermodynamic properties of nanoparticles with modulated magnetic ordering are studied by Monte-Carlo methods. Temperature dependences for main thermodynamic parameters are obtained. We present the characteristic modulated structures of nanoparticles and calculate the parameters of these structures. Modulated structures in nanoparticles are compared with macroscopic systems.

Two‐Dimensional V‐VI Binary Nanosheets with Square Lattice: A Theoretical Investigation

2021 ◽  
Author(s):  
Xin Qiao ◽  
Xiaodong Lv ◽  
Yinan Dong ◽  
Yanping Yang ◽  
Fengyu Li
Keyword(s):  
Theoretical Investigation ◽  
Square Lattice ◽  
Two Dimensional

scholarly journals Structural Disorder and Collective Behavior of Two-Dimensional Magnetic Nanostructures

Nanomaterials ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1392
Author(s):  
David Gallina ◽  
G. M. Pastor
Keyword(s):  
Interaction Energy ◽  
Time Evolution ◽  
Magnetic Nanostructures ◽  
Thermal Quenching ◽  
Structural Disorder ◽  
Square Lattice ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Two Dimensional ◽  
Energy Landscapes

Structural disorder has been shown to be responsible for profound changes of the interaction-energy landscapes and collective dynamics of two-dimensional (2D) magnetic nanostructures. Weakly-disordered 2D ensembles have a few particularly stable magnetic configurations with large basins of attraction from which the higher-energy metastable configurations are separated by only small downward barriers. In contrast, strongly-disordered ensembles have rough energy landscapes with a large number of low-energy local minima separated by relatively large energy barriers. Consequently, the former show good-structure-seeker behavior with an unhindered relaxation dynamics that is funnelled towards the global minimum, whereas the latter show a time evolution involving multiple time scales and trapping which is reminiscent of glasses. Although these general trends have been clearly established, a detailed assessment of the extent of these effects in specific nanostructure realizations remains elusive. The present study quantifies the disorder-induced changes in the interaction-energy landscape of two-dimensional dipole-coupled magnetic nanoparticles as a function of the magnetic configuration of the ensembles. Representative examples of weakly-disordered square-lattice arrangements, showing good structure-seeker behavior, and of strongly-disordered arrangements, showing spin-glass-like behavior, are considered. The topology of the kinetic networks of metastable magnetic configurations is analyzed. The consequences of disorder on the morphology of the interaction-energy landscapes are revealed by contrasting the corresponding disconnectivity graphs. The correlations between the characteristics of the energy landscapes and the Markovian dynamics of the various magnetic nanostructures are quantified by calculating the field-free relaxation time evolution after either magnetic saturation or thermal quenching and by comparing them with the corresponding averages over a large number of structural arrangements. Common trends and system-specific features are identified and discussed.

Spin-Singlet Ground State in Two-Dimensional S=1/2 Frustrated Square Lattice: (CuCl)LaNb2O7

2005 ◽  
Vol 74 (6) ◽  
pp. 1702-1705 ◽  
Author(s):  
H. Kageyama ◽  
T. Kitano ◽  
N. Oba ◽  
M. Nishi ◽  
S. Nagai ◽  
...  
Keyword(s):  
Ground State ◽  
Square Lattice ◽  
Singlet Ground State ◽  
Two Dimensional ◽  
Spin Singlet

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

Molecular Dynamics Simulations of Shock-Defect Interactions in Two-Dimensional Nonreactive Crystals

1992 ◽  
Vol 296 ◽  
Author(s):  
Robert S. Sinkovits ◽  
Lee Phillips ◽  
Elaine S. Oran ◽  
Jay P. Boris
Keyword(s):  
Molecular Dynamics ◽  
Hexagonal Lattice ◽  
Square Lattice ◽  
Two Dimensional ◽  
Connection Machine ◽  
Defect Sites ◽  
Principal Axes ◽  
Shock Motion ◽  
Defect Interactions ◽  
Dynamics Simulations

AbstractThe interactions of shocks with defects in two-dimensional square and hexagonal lattices of particles interacting through Lennard-Jones potentials are studied using molecular dynamics. In perfect lattices at zero temperature, shocks directed along one of the principal axes propagate through the crystal causing no permanent disruption. Vacancies, interstitials, and to a lesser degree, massive defects are all effective at converting directed shock motion into thermalized two-dimensional motion. Measures of lattice disruption quantitatively describe the effects of the different defects. The square lattice is unstable at nonzero temperatures, as shown by its tendency upon impact to reorganize into the lower-energy hexagonal state. This transition also occurs in the disordered region associated with the shock-defect interaction. The hexagonal lattice can be made arbitrarily stable even for shock-vacancy interactions through appropriate choice of potential parameters. In reactive crystals, these defect sites may be responsible for the onset of detonation. All calculations are performed using a program optimized for the massively parallel Connection Machine.

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