Static and dynamic properties of systems with extended defects: two-loop approximation

Lawrie, Ian D.; Прудников, В. В.

doi:10.1088/0022-3719/17/10/007

Cited by 84 publications

(99 citation statements)

References 13 publications

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“…The same holds for the extended defects: indeed, the case m = 1 is to be analyzed separately as far as expressions (27), (28) contain poles at m = 1, and one arrives [18] at the √ ε-expansion for the critical exponents. In particular, the corresponding expressions for z can be given only to the lowest nontrivial order.…”

Section: B ε ε D -Expansionmentioning

confidence: 95%

“…[18]. For m < m c , the random FP R is stable and the expression for z ⊥ and anisotropy function ζ α for m = 1 read [18]: …”

Section: B ε ε D -Expansionmentioning

confidence: 99%

“…The description of the critical behavior of magnets with extended impurities carried out in Refs. [15,16,18,19] was based on the double expansion in two parameters ε, ε d , considering both to be of the same order of magnitude. Being quite clear technically, such a statement causes however certain cautions.…”

Section: Rg Studymentioning

confidence: 99%

“…Indeed, magnetic crystals often contain defects of a more complex structure: linear dislocations, disclinations, complexes of non-magnetic impurities, embedded in the matrix of the original crystal [14]. Theoretical studies of critical behavior of magnets containing such "extended" (macroscopic) defects have attracted considerable interest [15,16,17,18,19,20,21,22,23,24,25,26], however, a systematic experimental analysis still remains to be performed.…”

Section: Introductionmentioning

confidence: 99%

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Critical dynamics and effective exponents of magnets with extended impurities

et al. 2005

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We investigate the asymptotic and effective static and dynamic critical behavior of (d = 3)-dimensional magnets with quenched extended defects, correlated in ε d dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining d − ε 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.

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Section: B ε ε D -Expansionmentioning

confidence: 95%

“…[18]. For m < m c , the random FP R is stable and the expression for z ⊥ and anisotropy function ζ α for m = 1 read [18]: …”

Section: B ε ε D -Expansionmentioning

confidence: 99%

Section: Rg Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Critical dynamics and effective exponents of magnets with extended impurities

et al. 2005

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“…Since the borderline value n c between a diverging and nondiverging specific heat at space dimensions d = 3 lies between order parameter (OP) dimensions n = 1 (Ising model) and n = 2 (XY model) only the Ising case belongs to a new universality class. In consequence this result led to the conclusion that for the critical dynamics the coupling of conserved quantities to the OP is of no relevance [2,3]. The argument was the following: For the critical dynamics of a relaxational model it was shown [4,5,6] that the coupling to a conserved density (e.g.…”

mentioning

confidence: 99%

Critical dynamics of diluted relaxational models coupled to a conserved density

et al. 2005

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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. The critical behavior of pure systems might be changed by introducing imperfections like dilution, defects, etc. into a critical system. If such a change can be expected is answered by the Harris criterion [1] stating that a new diluted critical behavior appears if the specific heat of the pure system is diverging. The diluted critical behavior then has a nondiverging specific heat. Since the borderline value n c between a diverging and nondiverging specific heat at space dimensions d = 3 lies between order parameter (OP) dimensions n = 1 (Ising model) and n = 2 (XY model) only the Ising case belongs to a new universality class. In consequence this result led to the conclusion that for the critical dynamics the coupling of conserved quantities to the OP is of no relevance [2,3]. The argument was the following: For the critical dynamics of a relaxational model it was shown [4,5,6] that the coupling to a conserved density (e.g. the energy density) is relevant if the specific heat diverges. Due to dilution this is never the case and therefore the coupling is of no relevance. Therefore most of the papers considered only the relaxational dynamics of Ising systems [7,8,9,10] However this argumentation is based on the asymptotic properties of the diluted model. Experimental data and computer simulations made clear that in most cases one observes non-asymptotic critical behavior, described often by dilution dependent effective exponents (see e.g. [11,12]). In such a case the Harris criterion does not hold and therefore one has to consider in the dynamics the coupling to the conserved density and its effects on the effective critical behavior. In addition one is not restricted to the Ising case since already in statics the effective critical behavior for n > 1 is different from the pure case [12].There are two relevant parameters of model C: (i) the static coupling γ of the OP to the conserved density and (ii) a dynamic parameter, the time scale ratio w = Γ/λ where Γ is the relaxation rate of the OP and λ is the diffusion rate of the conserved density. From the renormalization group (RG) treatment of model C one knows that the one loop order does not give reliable results due to the stability of a fixed point with the time scale ratio w = ∞. In two loop (and higher) order it turns out that this fixed point is unstable and model C is characterized by strong and weak scaling regions for the dynamics at d = 3 [5,6]. Moreover it was shown that non-asymptotic effects are already prese...

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Exotic Glassy Phase in the Site‐Diluted Transverse Ising Model at Zero Temperature ?

Busiello¹,

Cesare²,

Lukierska‐Walasek³

et al. 1989

Physica Status Solidi (b)

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A self-consistent diagrammatic approach is used for studying the zero-temperature properties of the three-dimensional site-diluted transverse Ising model via a path-integral representation. It is found, that the peculiar competition between random and quantum fluctuations inhibites the occurrence of a second-order phase transition and a n exotic phase with some spin-glass-like characteristics appears. This should provide a plausible explanation of recent experiments on some mixed crystals.

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Static and dynamic properties of systems with extended defects: two-loop approximation

Cited by 84 publications

References 13 publications

Critical dynamics and effective exponents of magnets with extended impurities

Critical dynamics and effective exponents of magnets with extended impurities

Critical dynamics of diluted relaxational models coupled to a conserved density

Exotic Glassy Phase in the Site‐Diluted Transverse Ising Model at Zero Temperature ?

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