Journal of Communications Technology and Electronics

Investigation of the effect of frustration on the critical properties of the 3D Heisenberg antiferromagnetic model

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, М. К. Бадиев

Published Feb 1, 2009• 0 citations

Abstract

The critical properties of the 3D frustrated Heisenberg model on a layered triangular lattice with a variable interlayer exchange interaction are investigated for the ratio of the constants of the interlayer ( J ′) and intralayer ( J ) interactions that ranges within the interval R = | J ′/ J | = 0.01…1. The finite-dimensional scaling theory is applied for the calculation of all of the main static magnetic and chiral critical indexes. It is shown that the 3D frustrated Heisenberg model on a layered triangular lattice forms a new universality class of critical behavior. It is found that the universality class of this model’s critical behavior is retained for values of R as small as R = 0.05.

DOI: 10.1134/s1064226909020107

Related papers

Critical Properties in the Ising Model on a Triangular Lattice with the Variable Interlayer Exchange Interaction

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, М. К. Бадиев

Abstract Phase transitions and critical and thermodynamic properties of the three-dimensional antiferromagnetic Ising model on a layered triangular lattice with variable interlayer exchange interaction are studied by the replica algorithm of the Monte Carlo method. The studies are carried out for the ratios of the intralayer J1 and interlayer J2 exchange interactions in the range of r = J2/J1 = 0.01–1.0. It is established that a second-order phase transition is observed in the considered r interval. Using the finite size scaling theory, the static critical exponents of the heat capacity α, susceptibility γ, order parameter β, correlation radius ν, and Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is preserved in the interval of 0.05 < r ≤ 1.0. It was found that with a further decrease in the r value, a crossover from the three-dimensional critical behavior to the quasi-two-dimensional one is observed.

Physics of the Solid StateOct 1, 20193 citations

Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, V. K. Badiev

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J 1) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J 1/J| = 0–0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.

Journal of Experimental and Theoretical PhysicsAug 1, 201213 citations

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice

Рамазанов Магомедшейх Курбанович, Akai Kurbanovich Murtazaev

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice with allowance for intralayer next nearest neighbor interactions have been studied using the replica Monte Carlo algorithm. The character of phase transitions has been analyzed using the histogram method and the Binder cumulant method. It has been found that a transition from the collinear to paramagnetic phase in the model under study occurs as a second order phase transition. The statistical critical exponents of the specific heat α, susceptibility γ, order parameter β, and correlation radius ν, as well as the Fisher index η, have been calculated using the finite-size scaling theory. It has been shown that the three-dimensional Heisenberg model on the layered cubic lattice with allowance for the next nearest neighbor interaction belongs to the same universality class of the critical behavior as the antiferromagnetic Heisenberg model on a layered triangular lattice.

Journal of Experimental and Theoretical Physics LettersJul 1, 201729 citations

Critical properties of the antiferromagnetic layered Ising model on a cubic lattice with competing interactions

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович

The critical properties of the antiferromagnetic layered Ising model on a cubic lattice with regard to the nearest-neighbor and next-nearest-neighbor interactions are investigated by the Monte Carlo method using the replica algorithm. The investigations are carried out for the ratios of exchange nearest-neighbor and next-nearest-neighbor interactions r = J 2/J 1 in the range of 0 ≤ r ≤ 1.0. Using the finite-size scaling theory, the static critical indices of specific heat α, order parameter β, susceptibility γ, correlation radius ν, and Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is retained in the range of 0 ≤ r ≤ 0.4. It is established that the change in the next-nearest-neighbor interaction value in this model in the range of r > 0.8 leads to the same universality class as the three-dimensional fully frustrated Ising model on the cubic lattice.

Physics of the Solid StateSep 1, 20176 citations

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

М. К. Бадиев, Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.

Journal of Experimental and Theoretical PhysicsOct 1, 20169 citations

Критические свойства в модели Изинга на треугольной решетке с переменным межслойным обменным взаимодействием

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, М. К. Бадиев

The Monte Carlo replica algorithm studies of phase transitions and critical phenomenaofthe layered triangular antiferromagnetic Ising model withvariable interlayer exchange interaction. Investigations were carried out for the ratios of the value of the intralayerJ1 and interlayer J2 exchange interactions in the range of values r = J2 / J1 = 0.01 ÷ 1.0. It was found that in the above range r is observed second-order phase transition.Static critical exponents for the heat capacityα, susceptibility γ, order parameter β, correlation radius ν, and the Fisher exponent ηare computed by means of the finite-size scaling theory. It is shown that the universality class of the critical behavior of the model is maintained in the range of 0.05 <r≤1.0.The results obtained suggest that3D frustrated Ising models on stacked triangularlattice with interlayer-to-intralayer exchange ratio 0.05<r≤1.0. preserves the universality class of criticalbehavior. At lower r, a crossover from 3D to 2D criticalbehavior is observed.

Physics of the Solid StateJan 1, 20190 citations