The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D-ferromagnetic Ising model on three dimensional Voronoi-Delaunay lattices. It is assumed that the coupling factor $J$ varies with the distance $r$ between the first neighbors as $J(r) \propto e^{-ar}$ , with $a \ge 0$ . The critical exponents $γ/ν$ , $β/ν$ , and $ν$ are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure three-dimensional ferromegnetic Ising model.The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D-ferromagnetic Ising model on three dimensional Voronoi-Delaunay lattices. It is assumed that the coupling factor $J$ varies with the distance $r$ between the first neighbors as $J(r) \propto e^{-ar}$, with $a \ge 0$. The critical exponents $γ/ν$, $β/ν$, and $ν$ are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure three-dimensional ferromegnetic Ising model.

arXiv:cond-mat/0509303Sep 12, 20050 citations

Critical exponents for cubic and impure uniaxial crystals: most accurate (?) theoretical values

I. O. Mayer, Aleksandr Ivanovich Sokolov, B. N. Shalaev

RG functions are calculated up to 4-loop order in 3 and 2 dimensions to evaluate, within Chisholm-Borel resummation technique, critical exponents for cubic and impure uniaxial crystals and the order parameter critical dimensionality nc . For 3D impure Ising crystals γ = 1.326, v = 0.670, α = -0.011, β = 0.342, η = 0.034, while critical exponents of 3D cubic crystals practically coincide with those of the Heisenberg model; nc = 2.9. For 2D systems the fermion representation enables us to find that their critical behavior is identical to that of pure Ising model, apart some logarithmic factors.RG functions are calculated up to 4-loop order in 3 and 2 dimensions to evaluate, within Chisholm-Borel resummation technique, critical exponents for cubic and impure uniaxial crystals and the order parameter critical dimensionality nc . For 3D impure Ising crystals γ = 1.326, v = 0.670, α = -0.011, β = 0.342, η = 0.034, while critical exponents of 3D cubic crystals practically coincide with those of the Heisenberg model; nc = 2.9. For 2D systems the fermion representation enables us to find that their critical behavior is identical to that of pure Ising model, apart some logarithmic factors.

FerroelectricsJul 1, 198969 citations

New estimates on various critical/universal quantities of the 3D Ising model

M. Hasenbusch, K. Pinn

arXiv:hep-lat/9709008Nuclear Physics B - Proceedings SupplementsApr 1, 19983 citations

Universality in two-dimensional Ising models

Henk W. J. Blöte, M. P. Nightingale

Physica A Statistical Mechanics and its ApplicationsDec 1, 198540 citations

Critical behavior of the 2D Ising model modulated by the Octonacci sequence

Gladstone Alencar Alves, M.S. Vasconcelos, T. F. A. Alves

Abstract We investigated the Ising model on a square lattice with ferro and antiferromagnetic interactions modulated by the quasiperiodic Octonacci sequence in both directions of the lattice. We have applied the replica exchange Monte Carlo (parallel tempering) technique to calculate the thermodynamic quantities of the system. We obtained the order parameter, the associated magnetic susceptibility ( χ ) and the specific heat ( c ) in order to characterize the universality class of the phase transition. Also, we use the finite size scaling method to obtain the critical temperature of the system and the critical exponents β , γ and ν . In the low temperature limit we have obtained a continuous transition with critical temperature around T c ≈ 1.413 . The system obeys the Ising universality class with logarithmic corrections. We found estimatives for the correction exponents β ^ , γ ^ and λ ^ by using the finite size scaling technique.Abstract We investigated the Ising model on a square lattice with ferro and antiferromagnetic interactions modulated by the quasiperiodic Octonacci sequence in both directions of the lattice. We have applied the replica exchange Monte Carlo (parallel tempering) technique to calculate the thermodynamic quantities of the system. We obtained the order parameter, the associated magnetic susceptibility ( χ ) and the specific heat ( c ) in order to characterize the universality class of the phase transition. Also, we use the finite size scaling method to obtain the critical temperature of the system and the critical exponents β , γ and ν . In the low temperature limit we have obtained a continuous transition with critical temperature around T c ≈ 1.413 . The system obeys the Ising universality class with logarithmic corrections. We found estimatives for the correction exponents β ^ , γ ^ and λ ^ by using the finite size scaling technique.

arXiv:1709.07870Journal of Statistical Mechanics Theory and ExperimentDec 1, 20172 citations

J

varies with the distance

r

between the first neighbors as

J(r) \propto e^{-ar}

, with

a \ge 0

. The critical exponents

γ/ν

β/ν

, and

ν

are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure three-dimensional ferromegnetic Ising model.