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Diffusion and defect data, solid state data. Part B, Solid state phenomena/Solid state phenomena

Phase Transitions in the Antiferromagnetic Heisenberg Model on a Triangular Lattice with the Next-Nearest Neighbor Interactions

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович

Published Apr 1, 2014• 0 citations
Publisher

Abstract

The critical behavior and phase transitions (PT) of the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with nearest-neighbor (J) and next-to-nearest neighbor (J1) interactions is studied by the replica Monte Carlo method. The first order phase transition has been revealed in the studied model based on the histogram method of processing data of the Monte Carlo for systems with large linear dimensions. Shown that the system exhibits the pseudouniversal critical behavior in the case of small lattices.

DOI
10.4028/www.scientific.net/ssp.215.3

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The critical behavior and phase transitions (PT) of the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with nearest-neighbor (J) and next-to-nearest neighbor (J1) interactions is studied by the replica Monte Carlo method. The first order phase transition has been revealed in the studied model based on the histogram method of processing data of the Monte Carlo for systems with large linear dimensions. Shown that the system exhibits the pseudouniversal critical behavior in the case of small lattices.
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.
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.
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.
Phase transitions and critical characteristics of the layered antiferromagnetic Ising model in the case of a cubic lattice with next-nearest-neighbor intralayer interactions are studied in the framework of the Monte Carlo method implementing the replica algorithm. The characteristics of the phase transitions are analyzed within the histogram method and with the Binder cumulants. For the model under study, it is found that the transition from the superantiferromagnetic phase to the paramagnetic one is a second order phase transition. The static critical exponents for the specific heat α, susceptibility γ, order parameter β, correlation radius ν, and the Fisher exponent η are calculated using the finite-size scaling theory. It is shown that the three-dimensional Ising model for the cubic lattice with next-nearest-neighbor interactions belongs to the same universality class of critical behavior as the completely frustrated three-dimensional Ising model.
Based on the replica algorithm by the Monte Carlo method, a computer simulation of the three-dimensional antiferromagnetic Heisenberg model is performed, taking into account the interactions of the first and second nearest neighbors. The phase transitions of this model are studied. The investigations were carried out for the ratios of the exchange interactions of the first and second nearest neighbors r=J2/J1r = J_2 / J_1r=J2​/J1​ in the range 0.0≤r≤1.00.0 \leq r \leq 1.00.0≤r≤1.0. The phase diagram of the critical temperature dependence on a value of the next-nearest neighbor interaction is plotted.
Phase transitions of the layered antiferromagnetic Ising model on a cubic lattice with allowance for intralayer next nearest neighbor interactions in the range of 0.0 ⩽ r < 1.0 have been studied on the basis of the replica algorithm by the Monte Carlo method. The character of phase transitions has been analyzed on the basis of the histogram method and the Binder cumulant method. The phase diagram of the dependence of the critical temperature on the next nearest neighbor interaction has been constructed. It has been shown that a secondorder phase transition is observed in the interval of 0.0 ⩽ r ⩽ 0.5 and for the value r = 0.9 and a first-order phase transition is observed in the interval of 0.6 ⩽ r < 0.8.