Critical crossover phenomena in disordered Ising systems

Heuer, H.-O.

doi:10.1088/0305-4470/26/6/007

Cited by 72 publications

(105 citation statements)

References 29 publications

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“…Critical exponents associated with the random fixed point have been investigated for dilution-type disorder by experimental, 2,3,4) theoretical 5,6) and numerical approaches. 7,8) Recently, extensive Monte Carlo (MC) studies 8) have clarified that the critical exponents of the 3D site-diluted Ising model are independent of the concentration of the site dilution p, suggesting the existence of a random fixed point. These results were obtained by carefully taking into account correction for finite-size scaling, unless the exponents clearly depended on p. 8) Experimentally, the critical exponents of randomly diluted antiferromagnetic Ising compounds, Fe x Zn 1−x F 2 3, 4) and Mn x Zn 1−x F 2 ,…”

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confidence: 99%

Random Fixed Point of Three-Dimensional Random-Bond Ising Models

Hukushima

2000

J. Phys. Soc. Jpn.

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The fixed-point structure of three-dimensional bond-disordered Ising models is investigated using the numerical domain-wall renormalization-group method. It is found that, in the ±J Ising model, there exists a non-trivial fixed point along the phase boundary between the paramagnetic and ferromagnetic phases. The fixed-point Hamiltonian of the ±J model numerically coincides with that of the unfrustrated random Ising models, strongly suggesting that both belong to the same universality class. Another fixed point corresponding to the multicritical point is also found in the ±J model. Critical properties associated with the fixed point are qualitatively consistent with theoretical predictions.KEYWORDS: domain wall renormalization group, fixed point, random system, spin glass, MC simulationThe influence of quenched disorder on model systems has attracted considerable interest in the field of statistical physics. The first remarkable criterion was given by Harris, 1) who claimed that if the specific-heat exponent α pure of the pure system is positive, disorder becomes relevant, implying that a new random fixed point governs critical phenomena of the random system. One of the simplest models belonging to such a class is the three-dimensional (3D) Ising model. Critical exponents associated with the random fixed point have been investigated for dilution-type disorder by experimental, 2, 3, 4) theoretical 5, 6) and numerical approaches. 7,8) Recently, extensive Monte Carlo (MC) studies 8) have clarified that the critical exponents of the 3D site-diluted Ising model are independent of the concentration of the site dilution p, suggesting the existence of a random fixed point. These results were obtained by carefully taking into account correction for finite-size scaling, unless the exponents clearly depended on p.8) Experimentally, the critical exponents of randomly diluted antiferromagnetic Ising compounds, Fe x Zn 1−x F 2 3, 4) and Mnare distinct from those of the pure 3D Ising model. While the existence of the random fixed point has been established for the 3D site-diluted Ising model, the idea of the universality class for random systems, namely classification by fixed points, has not been explored yet as compared with various pure systems. In particular, the question as to whether the random fixed point is universal irrespective of the type of disorder or not is a non-trivial problem. In the present work, we study critical phenomena associated with the ferromagnetic phase transition in 3D site-and bond-diluted and ±J Ising models. The main purpose is to determine the fixed-point structure of 3D random-bond Ising models by making use of a numerical renormalization-group (RG) analysis. Our strategy is based on the domain-wall RG (DWRG) method proposed by McMillan.9, 10) This method has been applied to a 2D frustrated randombond Ising model 9, 10) where there is no random fixed point, and recently to a 2D ± J frustrated random-bond three-state Potts model 11) which displays a non-trivial random fixed point. In this paper,...

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confidence: 99%

Random Fixed Point of Three-Dimensional Random-Bond Ising Models

Hukushima

2000

J. Phys. Soc. Jpn.

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“…And because of the triviality of the annealed disorder in the sense mentioned above, the most interesting object for study is just the quenched Ising model. The appearance of a set of new critical exponents for that model at d = 3 is confirmed by the experiments [29][30][31], renormalization group (RG) calculations [32][33][34][35][36][37][38][39][40][41], Monte-Carlo (M C) [42][43][44][45][46] and M CRG [47] simulations.…”

Section: Introductionmentioning

confidence: 75%

Untitled

Holovatch

Yavors’kii

1998

Journal of Statistical Physics

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Within the massive field theoretical renormalization group approach the expressions for the β-and γ-functions of the anisotropic mn-vector model are obtained for general space dimension d in three-loop approximation. Resumming corresponding asymptotic series, critical exponents for the case of the weakly diluted quenched Ising model (m = 1, n = 0), as well as estimates for the marginal order parameter component number m c of the weakly diluted quenched m-vector model are calculated as functions of d in the region 2 ≤ d < 4. Conclusions concerning the effectiveness of different resummation techniques are drawn.

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“…Values of z from paper [27] with EXP results agree rather well with our results only for weakly diluted systems with p = 0.95, while a noticeable difference of the results is observed for strongly disordered systems. Starting from the universality concept for critical behavior of diluted Ising systems and that the asymptotic value of z is independent of the dilution degree, the author in [28] obtained the asymptotic value z = 2.41 using the effective values of the exponent listed in Table II. The off-equilibrium critical dynamics of the 3D Ising model with the spin concentration varying in a wide range was analyzed in [29].…”

Section: Analysis Of Results and Conclusionmentioning

confidence: 99%