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Solid State Communications

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

Рамазанов Магомедшейх Курбанович, Akai Kurbanovich Murtazaev, М. А. Магомедов

Published Feb 22, 2016• 38 citations
Publisher
DOI
10.1016/j.ssc.2016.02.012

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Phase transitions in magnetic systems are studied using a Monte Carlo computer simulation method. The fundamentals of the technique are described and the strengths and limitations of this approach are discussed. Comparisons are made between the Monte Carlo data and exact results for the Ising square lattice. The properties of several different types of anisotropic systems are determined with particular care taken near the critical temperature Tc Competing interactions between neighboring sites has the effect of shifting Tc and may, in some cases, even change the nature of the ordered magnetic state. Critical field boundaries are traced out for several antiferromagnets and we show how competing interactions may give rise to tricritical points. We also present data on systems with impurities and examine the effects of free surfaces on the phase transition. Lastly we show how the transformation from the 2-dim Ising model to its lattice-gas model equivalent allows us to study adsorbed gas monolayers.

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Using the Monte Carlo Simulation (MCS) method combined with the Metropolis algorithm, we explore the magnetic properties of a two-dimensional (2D) spin system with spins 1, 2 and 3. The adapted simulation to the Ising model aims to study the impact of the correction term a of the interaction with second neighbors and the crystal field D on the critical temperature [Formula: see text] of the 2D anisotropic square lattice for different integer values of spins. The obtained results demonstrate that the critical temperature [Formula: see text] is significantly affected by the competing interactions between the anisotropy parameter, second-neighbor interaction and the crystal field. The considered model exhibits a critical phase transition regardless of the spin S value where the critical temperature increases with the value of S. Note that this phase transition occurs under the condition [Formula: see text]. Moreover, the obtained results show that the complex interactions give rise to a variety of phase diagrams, thereby revealing the richness of possible magnetic behaviors in the studied system.

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Phase Transitions in 2D Ising Model with Competing Interactions

BioChem Press

Motivation. 2D Ising model with competing interactions describes the thermodynamic properties of confined complex liquids like microemulsion films and some compounds of rare-earth metals. On the other hand there is a close relationship between critical properties of this model and peculiarities of the energy spectra of some onedimensional quantum models Therefore correct description of model phase diagram is of wide interest. Method. Density matrix renormalization group method for two-dimensional classical systems. Results. A new modification of density matrix renormalization scheme for 2D Ising model with competing interactions has been presented. The estimations for critical temperatures of second order phase transitions in the model were obtained. Conclusions. 2D Ising model with competing interactions has a complicated phase diagram and can be described by means of corresponding version of DMRG method at least in the vicinity of some critical points.

•Jan 1, 2003•0 citations
Phase transitions in magnetic systems are studied using a Monte Carlo computer simulation method. The fundamentals of the technique are described and the strengths and limitations of this approach are discussed. Comparisons are made between the Monte Carlo data and exact results for the Ising square lattice. The properties of several different types of anisotropic systems are determined with particular care taken near the critical temperature Tc Competing interactions between neighboring sites has the effect of shifting Tc and may, in some cases, even change the nature of the ordered magnetic state. Critical field boundaries are traced out for several antiferromagnets and we show how competing interactions may give rise to tricritical points. We also present data on systems with impurities and examine the effects of free surfaces on the phase transition. Lastly we show how the transformation from the 2-dim Ising model to its lattice-gas model equivalent allows us to study adsorbed gas monolayers.
Using the Monte Carlo Simulation (MCS) method combined with the Metropolis algorithm, we explore the magnetic properties of a two-dimensional (2D) spin system with spins 1, 2 and 3. The adapted simulation to the Ising model aims to study the impact of the correction term a of the interaction with second neighbors and the crystal field D on the critical temperature [Formula: see text] of the 2D anisotropic square lattice for different integer values of spins. The obtained results demonstrate that the critical temperature [Formula: see text] is significantly affected by the competing interactions between the anisotropy parameter, second-neighbor interaction and the crystal field. The considered model exhibits a critical phase transition regardless of the spin S value where the critical temperature increases with the value of S. Note that this phase transition occurs under the condition [Formula: see text]. Moreover, the obtained results show that the complex interactions give rise to a variety of phase diagrams, thereby revealing the richness of possible magnetic behaviors in the studied system.
Motivation. 2D Ising model with competing interactions describes the thermodynamic properties of confined complex liquids like microemulsion films and some compounds of rare-earth metals. On the other hand there is a close relationship between critical properties of this model and peculiarities of the energy spectra of some onedimensional quantum models Therefore correct description of model phase diagram is of wide interest. Method. Density matrix renormalization group method for two-dimensional classical systems. Results. A new modification of density matrix renormalization scheme for 2D Ising model with competing interactions has been presented. The estimations for critical temperatures of second order phase transitions in the model were obtained. Conclusions. 2D Ising model with competing interactions has a complicated phase diagram and can be described by means of corresponding version of DMRG method at least in the vicinity of some critical points.