M. Dudka

Publications (18)4.51 Total impact

• Article: Marginal dimensions for multicritical phase transitions

  M. Dudka, R. Folk, Yu. Holovatch, G. Moser
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  ABSTRACT: The field-theoretical model describing multicritical phenomena with two coupled order parameters with n_{||} and n_{\perp} components and of O(n_{||}) \oplus O(n_{\perp}) symmetry is considered. Conditions for realization of different types of multicritical behaviour are studied within the field-theoretical renormalization group approach. Surfaces separating stability regions for certain types of multicritical behaviour in parametric space of order parameter dimensions and space dimension d are calculated using the two-loop renormalization group functions. Series for the order parameter marginal dimensions that control the crossover between different universality classes are extracted up to the fourth order in \varepsilon=4-d and to the fifth order in a pseudo-\varepsilon parameter using the known high-order perturbative expansions for isotropic and cubic models. Special attention is paid to a particular case of O(1) \oplus O(2) symmetric model relevant for description of anisotropic antiferromagnets in an external magnetic field.
  06/2012;
• Source

  Available from: ArXiv

  Article: Analysis of the 3d massive renormalization group perturbative expansions: a delicate case

  B. Delamotte, M. Dudka, Yu. Holovatch, D. Mouhanna
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  ABSTRACT: The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the antiferromagnetic model defined on the stacked triangular lattice. We consider all models at fixed d=3 and analyze the resummation procedures currently used to compute the critical exponents. We first show that, for the O(N) model, the resummation does not eliminate all non-physical (spurious) fixed points (FPs). Then the dependence of spurious as well as of the Wilson-Fisher FPs on the resummation parameters is carefully studied. The critical exponents at the Wilson-Fisher FP show a weak dependence on the resummation parameters. On the contrary, the exponents at the spurious FP as well as its very existence are strongly dependent on these parameters. For the cubic model, a new stable FP is found and its properties depend also strongly on the resummation parameters. It appears to be spurious, as expected. As for the frustrated models, there are two cases depending on the value of the number of spin components. When N is greater than a critical value Nc, the stable FP shows common characteristic with the Wilson-Fisher FP. On the contrary, for N<Nc, the results obtained at the stable FP are similar to those obtained at the spurious FPs of the O(N) and cubic models. We conclude from this analysis that the stable FP found for N 3, we conclude that the transitions for XY and Heisenberg frustrated magnets are of first order.
  12/2010;
• Source

  Available from: ArXiv

  Article: About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

  B. Delamotte, M. Dudka, Yu. Holovatch, D. Mouhanna
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  ABSTRACT: We show that the critical behaviour of two- and three-dimensional frustrated magnets cannot reliably be described from the known five- and six-loops perturbative renormalization group results. Our conclusions are based on a careful re-analysis of the resummed perturbative series obtained within the zero momentum massive scheme. In three dimensions, the critical exponents for XY and Heisenberg spins display strong dependences on the parameters of the resummation procedure and on the loop order. This behaviour strongly suggests that the fixed points found are in fact spurious. In two dimensions, we find, as in the O(N) case, that there is apparent convergence of the critical exponents but towards erroneous values. As a consequence, the interesting question of the description of the crossover/transition induced by Z2 topological defects in two-dimensional frustrated Heisenberg spins remains open. Comment: 18 pages, 30 figures
  09/2010;
• Article: Dynamic scaling functions and amplitude ratios of stochastic models with energy conservation above Tc.

  M Dudka, R Folk, G Moser
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  ABSTRACT: Dynamical scaling functions above Tc for the characteristic frequencies and the dynamical correlation functions of the order parameter and the conserved density of model C are calculated in one loop order. By a proper exponentiation procedure these results can be extended in order to consider the changes in these functions using the fixed point values and exponents in two loop order. The dynamical amplitude ratio R of the characteristic frequencies is generalized to the critical region. Surprisingly the decay of the shape functions at large scaled frequency does not behave as expected from applying scaling arguments. The exponent upsilon of the decay does not change when going from the critical to the hydrodynamic region although the shape functions change. The value of upsilon for the order parameter is in agreement with its value in the critical region, whereas for the conserved density it is equal to 2, the value in the hydrodynamic region.
  Physical Review E 09/2009; 80(3 Pt 1):031124. · 2.26 Impact Factor
• Source

  Available from: ArXiv

  Article: Model C critical dynamics of random anisotropy magnets

  M. Dudka, R. Folk, Yu. Holovatch, G. Moser
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  ABSTRACT: We study the relaxational critical dynamics of the three-dimensional random anisotropy magnets with the non-conserved n-component order parameter coupled to a conserved scalar density. In the random anisotropy magnets the structural disorder is present in a form of local quenched anisotropy axes of random orientation. When the anisotropy axes are randomly distributed along the edges of the n-dimensional hypercube, asymptotical dynamical critical properties coincide with those of the random-site Ising model. However structural disorder gives rise to considerable effects for non-asymptotic critical dynamics. We investigate this phenomenon by a field-theoretical renormalization group analysis in the two-loop order. We study critical slowing down and obtain quantitative estimates for the effective and asymptotic critical exponents of the order parameter and scalar density. The results predict complex scenarios for the effective critical exponent approaching an asymptotic regime. Comment: 8 figures, style files included
  04/2007;
• Source

  Available from: icmp.lviv.ua

  Article: Gauge Dependence of the Critical Dynamics at the Superconducting Transition

  M. Dudka, R. Folk, G. Moser
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  ABSTRACT: The critical dynamics of superconductors in the charged regime is reconsidered within field-theory. For the dynamics the Ginzburg-Landau model with complex order parameter coupled to the gauge field suggested earlier [Lannert et al. Phys. Rev. Lett. 92, 097004 (2004)] is used. Assuming relaxational dynamics for both quantities the renormalization group functions within one loop approximation are recalculated for different choices of the gauge. A gauge independent result for the divergence of the measurable electric conductivity is obtained only at the weak scaling fixed point unstable in one loop order where the time scales of the order parameter and the gauge field are different.
  01/2007;
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  Available from:

  Article: Model C critical dynamics of disordered magnets

  M. Dudka, R. Folk, Yu. Holovatch, G. Moser
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  ABSTRACT: The critical dynamics of model C in the presence of disorder is considered. It is known that in the asymptotics a conserved secondary density decouples from the nonconserved order parameter for disordered systems. However couplings between order parameter and secondary density cause considerable effects on non-asymptotic critical properties. Here, a general procedure for a renormalization group treatment is proposed. Already the one-loop approximation gives a qualitatively correct picture of the diluted model C dynamical criticality. A more quantitative description is achieved using two-loop approximation. In order to get reliable results resummation technique has to be applied. Comment: 21 page, 4 figures, submitted to the proceedings of the conference "Renormalization Group 2005", Helsinki, Finland, 30 August - 3 September 2005
  01/2006;
• Article: Critical dynamics of diluted relaxational models coupled to a conserved density.

  M Dudka, R Folk, Yu Holovatch, G Moser
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  ABSTRACT: We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a nonconserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to model A critical dynamics in the asymptotics; however, it is the effective critical behavior that is often observed in experiments and in computer simulations, and this is described by the full set of dynamical equations of diluted model C. Indeed, different scenarios of effective critical behavior are predicted.
  Physical Review E 10/2005; 72(3 Pt 2):036107. · 2.26 Impact Factor
• Source

  Available from: arxiv.org

  Article: Enhancement of the critical slowing down influenced by extended defects

  V. Blavatska, M. Dudka, R. Folk, Yu. Holovatch
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  ABSTRACT: We study an influence of the quenched extended defects on the critical dynamics of the d=3-dimensional systems with m-component non-conserved order parameter (model A dynamics). Considering defects to be correlated in \epsilon_d dimensions and randomly distributed in d-\epsilon_d dimensions we obtain reliable numerical values for the critical exponents governing divergence of the relaxation time as function of m and \epsilon_d. Comment: Submitted to the Proceedings of the 3rd International Conference "Physics of Liquid Matter: Modern Problems", May 27-31, 2005, Kyiv, Ukraine
  08/2005;
• Source

  Available from: arxiv.org

  Article: Critical slowing down in random anisotropy magnets

  M. Dudka, R. Folk, Yu. Holovatch, G. Moser
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  ABSTRACT: 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 influences 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 $z_{\rm eff}$.
  08/2005;
• Source

  Available from: arxiv.org

  Article: Critical dynamics and effective exponents of magnets with extended impurities

  V. Blavats'ka, M. Dudka, R. Folk, Yu. Holovatch
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  ABSTRACT: We investigate the asymptotic and effective static and dynamic critical behavior of (d=3)-dimensional magnets with quenched extended defects, correlated in $\epsilon_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-\epsilon_d$ dimensions. The field-theoretical renormalization group perturbative expansions being evaluated naively do not allow for the reliable numerical data. We apply the Chisholm-Borel resummation technique to restore convergence of the two-loop expansions and report the numerical values of the asymptotic critical exponents for the model A dynamics. We discuss different scenarios for static and dynamic effective critical behavior and give values for corresponding non-universal exponents. Comment: 12 pages, 6 figures
  06/2005;
• Source

  Available from: arxiv.org

  Article: Effective critical behaviour of diluted Heisenberg-like magnets

  M. Dudka, R. Folk, Yu. Holovatch, D. Ivaneiko
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  ABSTRACT: In agreement with the Harris criterion, asymptotic critical exponents of three-dimensional (3d) Heisenberg-like magnets are not influenced by weak quenched dilution of non-magnetic component. However, often in the experimental studies of corresponding systems concentration- and temperature-dependent exponents are found with values differing from those of the 3d Heisenberg model. In our study, we use the field--theoretical renormalization group approach to explain this observation and to calculate the effective critical exponents of weakly diluted quenched Heisenberg-like magnet. Being non-universal, these exponents change with distance to the critical point $T_c$ as observed experimentally. In the asymptotic limit (at $T_c$) they equal to the critical exponents of the pure 3d Heisenberg magnet as predicted by the Harris criterion. Comment: 15 pages, 4 figures
  06/2005;
• Source

  Available from: arxiv.org

  Article: Critical dynamics of diluted relaxational models coupled to a conserved density (diluted model C)

  M. Dudka, R. Folk, Yu. Holovatch, G. Moser
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  ABSTRACT: We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a non-conserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to model A critical dynamics in the asymptotics, however it is the effective critical behavior which is often observed in experiments and in computer simulations and this is described by the full set of dynamical equations of diluted model C. Indeed different scenarios of effective critical behavior are predicted. Comment: 4 pages, 5 figures
  06/2005;
• Source

  Available from: arxiv.org

  Article: Critical properties of random anisotropy magnets

  M. Dudka, R. Folk, Yu. Holovatch
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  ABSTRACT: 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.
  Journal of Magnetism and Magnetic Materials. 06/2004;
• Source

  Available from: ArXiv

  Article: Universality classes of three-dimensional $mn$-vector model

  M. Dudka, Yu. Holovatch, T. Yavors'kii
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  ABSTRACT: We study the conditions under which the critical behavior of the three-dimensional $mn$-vector model does not belong to the spherically symmetrical universality class. In the calculations we rely on the field-theoretical renormalization group approach in different regularization schemes adjusted by resummation and extended analysis of the series for renormalization-group functions which are known for the model in high orders of perturbation theory. The phase diagram of the three-dimensional $mn$-vector model is built marking out domains in the $mn$-plane where the model belongs to a given universality class. Comment: 9 pages, 1 figure
  04/2004;
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  Available from: arxiv.org

  Article: A Marginal Dimension of a Weakly Diluted Quenched m-Vector Model

  Yu. Holovatch, M. Dudka, T. Yavors'kii
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  ABSTRACT: We calculate a marginal order parameter dimension $m_c$ which in a weakly diluted quenched $m$-vector model controls the crossover from a universality class of a ``pure'' model ($m>m_c$) to a new universality class ($m<m_c$). Exploiting the Harris criterion and the field-theoretical renormalization group approach allows us to obtain $m_c$ as a five-loop $\epsilon$-expansion as well as a six-loop pseudo-$\epsilon$ expansion. In order to estimate the numerical value of $m_c$ we process the series by precisely adjusted Pad\'e--Borel--Leroy resummation procedures. Our final result $m_c=1.912\pm0.004<2$ stems from the longer and more reliable pseudo-$\epsilon$ expansion, suggesting that a weak quenched disorder does not change the values of $xy$-model critical exponents as it follows from the experiments on critical properties of ${\rm He}^4$ in porous media.
  05/2002;
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  Available from: arxiv.org

  Article: Weak quenched disorder and criticality: resummation of asymptotic(?) series

  Yu. Holovatch, V. Blavats'ka, M. Dudka, C. von Ferber, R. Folk, T. Yavors'kii
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  ABSTRACT: In these lectures, 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 these lectures is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models. Comment: Lectures given at the Second International Pamporovo Workshop on Cooperative Phenomena in Condensed Matter (28th July - 7th August 2001, Pamporovo, Bulgaria). 51 pages, 12 figures, 1 style files included
  11/2001;
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  Available from: arxiv.org

  Article: Phase Transition in the Random Anisotropy Model

  M. Dudka, R. Folk, Yu. Holovatch
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  ABSTRACT: The influence of a local anisotropy of random orientation on a ferromagnetic phase transition is studied for two cases of anisotropy axis distribution. To this end a model of a random anisotropy magnet is analyzed by means of the field theoretical renormalization group approach in two loop approximation refined by a resummation of the asymptotic series. The one-loop result of Aharony indicating the absence of a second-order phase transition for an isotropic distribution of random anisotropy axis at space dimension $d<4$ is corroborated. For a cubic distribution the accessible stable fixed point leads to disordered Ising-like critical exponents.
  07/2001;