On the Critical Behaviour of Random Anisotropy Magnets: Cubic Anisotropy

Dudka,; Folk,; Holovatch,

doi:10.5488/cmp.4.3.459

Cited by 11 publications

(27 citation statements)

References 17 publications

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“…This picture found its further confirmation by the fixed d approach in the twoloop [75,76,102] and later in the five-loop [77] approximation of the massive scheme. The minimal subtraction scheme corroborates these results.…”

Section: Cubic Distributionmentioning

confidence: 79%

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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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Section: Cubic Distributionmentioning

confidence: 79%

“…The last degeneracy was observed also for the diluted cubic model [122,123]. This implies a √ ε-expansion [115,116] for the FPs [75,76,102] rather than an ε-expansion. Among the FPs found with the help of the √ ε-expansion, the FP with coordinates w * < 0, y * > 0, u * = v * = 0 is stable.…”

Section: Cubic Distributionmentioning

confidence: 91%

Critical properties of random anisotropy magnets

Dudka

Folk

Holovatch

2005

Journal of Magnetism and Magnetic Materials

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“…In the limiting cases, the obtained results reproduce the known ones. 45,[50][51][52] Unlike the one-loop approximation, where we know the number of solutions, here we solve the system of nonalgebraic equations and thus the number of FPs is un-known in advance. Nevertheless we keep the notation of FPs used in Table II.…”

Section: B Two-loop Approximationmentioning

confidence: 99%

Possibility of a continuous phase transition in random-anisotropy magnets with a generic random-axis distribution

et al. 2020

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We reconsider the problem of the critical behavior of a three-dimensional O(m) symmetric magnetic system in the presence of random anisotropy disorder with a generic trimodal random axis distribution. By introducing n replicas to average over disorder it can be coarse-grained to a φ 4theory with m × n component order parameter and five coupling constants taken in the limit of n → 0. Using a field theory approach we renormalize the model to two-loop order and calculate the β-functions within the ε expansion and directly in three dimensions. We analyze the corresponding renormalization group flows with the help of the Padé-Borel resummation technique. We show that there is no stable fixed point accessible from physical initial conditions whose existence was argued in the previous studies. This indicates an absence of a long-range ordered phase in the presence of random anisotropy disorder with a generic random axis distribution. arXiv:1910.14461v1 [cond-mat.dis-nn]

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“…subsection 6.1) of the weakly diluted quenched Ising model. The √ ε expansion of the fixed point XVII holds only for m = 2 and is caused by the one-loop degeneracy of the β u , β v , β y functions for w = 0 (c. f. singularity at m = 2 in the ε-expansion of the fixed point IX) 128 .…”

Section: Critical Behaviour Of Stanley Model With Random Anisotropymentioning

confidence: 99%

“…Resummed values of the fixed points and critical exponents for cubic distribution in two-loop approximation for d = 3127,128 .FP m u…”

mentioning

confidence: 99%

Weak Quenched Disorder and Criticality: Resummation of Asymptotic(?) Series

Holovatch

Blavatska

Dudka

et al. 2002

Int. J. Mod. Phys. B

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In this review paper, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range-correlated random-site disorder, and (iii) random anisotropy.Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of this review is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.In contrast to the critical temperature, the values of the critical exponents do not depend on microscopic details of the Hamiltonian and are determined only by the global properties of the model. For a short-range interaction the global properties are the lattice dimension d, the dimension m and other symmetry properties of the order parameter. Due to the fact that the critical exponents may be identical November 9, 2018 10:37 WSPC/Guidelines lecture Weak quenched disorder and criticality: resummation of asymptotic(?) series 5

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On the Critical Behaviour of Random Anisotropy Magnets: Cubic Anisotropy

Cited by 11 publications

References 17 publications

Critical properties of random anisotropy magnets

Critical properties of random anisotropy magnets

Possibility of a continuous phase transition in random-anisotropy magnets with a generic random-axis distribution

Weak Quenched Disorder and Criticality: Resummation of Asymptotic(?) Series

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