Thermodynamic, critical properties and phase transitions of the Ising model on a square lattice with competing interactions

2016 ◽  
Vol 233 ◽  
pp. 35-40 ◽  
Author(s):  
M.K. Ramazanov ◽  
A.K. Murtazaev ◽  
M.A. Magomedov
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Square Lattice ◽  
Critical Properties ◽  
Competing Interactions

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.

Critical properties of a random transverse crystal field Ising model with bond dilution

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
Ling Wen ◽  
Yan Shi-Lei
Keyword(s):  
Ising Model ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Effective Field ◽  
Square Lattice ◽  
Critical Properties ◽  
Strong Bond ◽  
Ordered Phases ◽  
Bond Dilution ◽  
Global Phase Diagrams

AbstractWithin effective field theory (EFT), the critical properties of a random transverse crystal field Ising model with bond dilution are studied on a square lattice. Under both weak and strong bond dilution conditions, we consider three cases (α = 0,±0.5) of a transverse crystal field ratio, obtaining global phase diagrams in T−D x space for changes in the random transverse crystal field concentration. The phase diagrams obtained for a weak bond dilution are very similar in shape to those of pure bond but with decreases in corresponding ordered phases and critical values. However, the phase diagrams for a strong bond dilution exhibit varieties, including a change in reentrant phenomenon, the occurrence of transverse crystal field degeneration, and the opposite direction crossover of temperature peak value.

scholarly journals Weak Singularities of the Isothermal Entropy Change as the Smoking Gun Evidence of Phase Transitions of Mixed-Spin Ising Model on a Decorated Square Lattice in Transverse Field

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1533
Author(s):  
Jozef Strečka ◽  
Katarína Karl’ová
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
Ising Model ◽  
Magnetocaloric Effect ◽  
Entropy Change ◽  
Transverse Magnetic ◽  
Continuous Phase ◽  
Square Lattice ◽  
Mixed Spin ◽  
Weak Singularities

The magnetocaloric response of the mixed spin-1/2 and spin-S (S>1/2) Ising model on a decorated square lattice is thoroughly examined in presence of the transverse magnetic field within the generalized decoration-iteration transformation, which provides an exact mapping relation with an effective spin-1/2 Ising model on a square lattice in a zero magnetic field. Temperature dependencies of the entropy and isothermal entropy change exhibit an outstanding singular behavior in a close neighborhood of temperature-driven continuous phase transitions, which can be additionally tuned by the applied transverse magnetic field. While temperature variations of the entropy display in proximity of the critical temperature Tc a striking energy-type singularity (T−Tc)log|T−Tc|, two analogous weak singularities can be encountered in the temperature dependence of the isothermal entropy change. The basic magnetocaloric measurement of the isothermal entropy change may accordingly afford the smoking gun evidence of continuous phase transitions. It is shown that the investigated model predominantly displays the conventional magnetocaloric effect with exception of a small range of moderate temperatures, which contrarily promotes the inverse magnetocaloric effect. It turns out that the temperature range inherent to the inverse magnetocaloric effect is gradually suppressed upon increasing of the spin magnitude S.

Critical properties of an antiferromagnetic decorated Ising model on a square lattice

2020 ◽  
Vol 46 (10) ◽  
pp. 1016-1020
Author(s):  
V. A. Mutailamov ◽  
A. K. Murtazaev
Keyword(s):  
Ising Model ◽  
Square Lattice ◽  
Critical Properties

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.

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