On the Critical Behaviour of Random Anisotropy Magnets

Dudka,; Folk,; Holovatch,

doi:10.5488/cmp.4.1.77

Cited by 18 publications

(48 citation statements)

References 13 publications

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“…The absence of ferromagnetic ordering in isotropic RAM was first observed in the renormalization group study of [4] where no accessible fixed points of the renormalization group transformation were obtained for the model within ε = 4 − d expansion. Recently, this result was corroborated by higher-order calculations refined by a resummation technique [5]. The proof of [6,7] used arguments similar to those applied by Imry and Ma [8] for a random-field Ising model and showed that the susceptibility of the ordered state diverges for d < 4.…”

Section: Introductionmentioning

confidence: 79%

“…Note once more, that this behaviour is characteristic only of RAM with cubic distribution of random anisotropy axis, described by the effective Hamiltonian (5). A distribution of random anisotropy axis is relevant, i.e., for isotropic distribution, all investigations bring about an absence of a second order phase transition for d 4 [4][5][6][7][8][9][10]12].…”

Section: Discussionmentioning

confidence: 99%

“…We show the existence of a second order phase transition and make our conclusions about its numerical characteristics based on the resummation technique applied to the resulting perturbation theory series. The paper is a direct continuation of our preceding work [5], where we applied similar tools to study RAM with an isotropic distribution p(x) and we refer the reader there for a more extended review of the RAM general features.…”

Section: Introductionmentioning

confidence: 99%

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On the Critical Behaviour of Random Anisotropy Magnets: Cubic Anisotropy

Dudka¹,

Folk²,

Holovatch³

2001

Condens. Matter Phys.

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The critical behaviour of an m -vector model with a local anisotropy axis of random orientation is studied within the field-theoretical renormalization group approach for cubic distribution of anisotropy axis. Expressions for the renormalization group functions are calculated up to the two-loop order and investigated both by an ε = 4 − d expansion and directly at space dimension d = 3 by means of the Padé-Borel resummation. One accessible stable fixed point indicating a 2nd order ferromagnetic phase transition with dilute Ising-like critical exponents is obtained.

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Section: Introductionmentioning

confidence: 79%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Critical Behaviour of Random Anisotropy Magnets: Cubic Anisotropy

Dudka¹,

Folk²,

Holovatch³

2001

Condens. Matter Phys.

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“…In this case, there occurs the second order phase transition into the magnetically ordered low-temperature phase. Asymptotically it is characterized by the critical exponents of the random-site Ising model as suggested already in [27] and confirmed later in [28][29][30]. The studies of static criticality of random anisotropy magnets are far from being as intensive as those of the diluted magnets [10], and even less is known about their dynamic critical behaviour.…”

Section: Introductionmentioning

confidence: 75%

“…However, it may occur for an anisotropic distribution. In statics, this situation was corroborated by the RG studies of RAM [26][27][28][29][30] restrictingx to be pointed along one of the 2m directions of the axesk i of a hypercubic lattice (cubic distribution):…”

Section: Introductionmentioning

confidence: 84%

Critical slowing down in random anisotropy magnets

Dudka¹,

Folk²,

Holovatch³

et al. 2005

Condens. Matter Phys.

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We study the purely relaxational critical dynamics with non-conserved order parameter (model A critical dynamics) for three-dimensional magnets with disorder in a form of the random anisotropy axis. For the random axis anisotropic distribution, the static asymptotic critical behaviour coincides with that of random site Ising systems. Therefore the asymptotic critical dynamics is governed by the dynamical exponent of the random Ising model. However, the disorder effects considerably the dynamical behaviour in the non-asymptotic regime. We perform a field-theoretical renormalization group analysis within the minimal subtraction scheme in two-loop approximation to investigate asymptotic and effective critical dynamics of random anisotropy systems. The results demonstrate the non-monotonic behaviour of the dynamical effective critical exponent z eff .

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Critical properties of random anisotropy magnets

Dudka

Folk

Holovatch

2005

Journal of Magnetism and Magnetic Materials

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The problem of critical behaviour of three dimensional random anisotropy magnets, which constitute a wide class of disordered magnets is considered. Previous results obtained in experiments, by Monte Carlo simulations and within different theoretical approaches give evidence for a second order phase transition for anisotropic distributions of the local anisotropy axes, while for the case of isotropic distribution such transition is absent. This outcome is described by renormalization group in its field theoretical variant on the basis of the random anisotropy model. Considerable attention is paid to the investigation of the effective critical behaviour which explains the observation of different behaviour in the same universality class.Comment: 41 pages, 10 figure

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On the Critical Behaviour of Random Anisotropy Magnets

Cited by 18 publications

References 13 publications

On the Critical Behaviour of Random Anisotropy Magnets: Cubic Anisotropy

On the Critical Behaviour of Random Anisotropy Magnets: Cubic Anisotropy

Critical slowing down in random anisotropy magnets

Critical properties of random anisotropy magnets

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