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Critical indices for the two-dimensional Ising model with nearest-neighbor and next-nearest-neighbor interactions

Kazuyuki Tanaka, Tsuyoshi Horiguchi, Tohru Morita

Physics Letters AMay 1, 199226 citations

Critical Behavior of the Ising Model Close to Four Dimensions

Peter Kopietz, Lorenz Bartosch, Florian Schütz

Lecture notes in physicsDec 25, 20090 citations

Coherent-Anomaly Analysis with Cluster Variation Method for Two-Dimensional Ising Model with Nearest-Neighbor and Next-Nearest-Neighbor Interactions

Kazuyuki Tanaka, Tsuyoshi Horiguchi, Tohru Morita

The spin-pair correlation functions in the Ising model with nearest-neighbor interaction J>0 and next-nearest-neighbor interaction J′ on the square lattice are obtained in three approximations of the simplified cluster variation method. We estimate the critical indices ην, γ and ν, by applying the coherent-anomaly method to the obtained spin-pair correlation functions. We conclude that the system belongs to the Onsager universality class when J′/J > −0.5 and does not when J′/J < −0.5.The spin-pair correlation functions in the Ising model with nearest-neighbor interaction J>0 and next-nearest-neighbor interaction J′ on the square lattice are obtained in three approximations of the simplified cluster variation method. We estimate the critical indices ην, γ and ν, by applying the coherent-anomaly method to the obtained spin-pair correlation functions. We conclude that the system belongs to the Onsager universality class when J′/J > −0.5 and does not when J′/J < −0.5.

Progress of Theoretical Physics SupplementJan 1, 19942 citations

The critical index for the correlation length in the three-dimensional Ising model

I. P. Yukhnovskii, Mykhailo P. Kozlovskii

SPhDOct 1, 19770 citations

Next-Nearest-Neighbor Ising Model

R. W. Gibberd

The next-nearest-neighbor two-dimensional Ising model is cast into a form which resembles a one-dimensional interacting many-fermion system. An approximation, which has previously been shown to be successful in giving the critical properties of the two-dimensional ferroelectric problem, is used. From the approximate expression obtained, the critical indices are found to be α = α′ = 0, β = ⅛, which agrees with the results obtained from series expansions and plausible physical arguments. The critical temperature obtained agrees to within 6% of the series expansion results.The next-nearest-neighbor two-dimensional Ising model is cast into a form which resembles a one-dimensional interacting many-fermion system. An approximation, which has previously been shown to be successful in giving the critical properties of the two-dimensional ferroelectric problem, is used. From the approximate expression obtained, the critical indices are found to be α = α′ = 0, β = ⅛, which agrees with the results obtained from series expansions and plausible physical arguments. The critical temperature obtained agrees to within 6% of the series expansion results.

Journal of Mathematical PhysicsJun 1, 196930 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.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

Critical indices for the two-dimensional Ising model with nearest-neighbor and next-nearest-neighbor interactions

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Critical indices for the two-dimensional Ising model with nearest-neighbor and next-nearest-neighbor interactions

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