Browsing by Author "Schwabl, Franz"

Now showing 1 - 12 of 12
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    Continuous elastic phase transitions and disordered crystals
    Schwabl, Franz; Täuber, Uwe C. (1996-12-15)
    We review the theory of second–order (ferro–)elastic phase transitions, where the order parameter consists of a certain linear combination of strain tensor components, and the accompanying soft mode is an acoustic phonon. In three–dimensional crystals, the softening can occur in one– or two–dimensional soft sectors. The ensuing anisotropy reduces the effect of fluctuations, rendering the critical behaviour of these systems classical for a one–dimensional soft sector, and classical with logarithmic corrections in case of a two–dimensional soft sector. The dynamical critical exponent is z = 2, and as a consequence the sound velocity vanishes as cs ∝ |T − Tc|1/2, while the phonon damping coefficient is essentially temperature–independent. Even if the elastic phase transition is driven by the softening of an optical mode linearly coupled to a transverse acoustic phonon, the critical exponents retain their mean–field values. Disorder may lead to a variety of precursor effects and modified critical behaviour. Defects that locally soften the crystal may induce the phenomenon of local order parameter condensation. When the correlation length of the pure system exceeds the average defect separation nD−1/3, a disorder–induced phase transition to a state with non–zero average order parameter can occur at a temperature Tc(nD) well above the transition temperature T0c of the pure crystal. Near T0c, the order–parameter curve, susceptibility, and specific heat appear rounded. For T < Tc(nD) the spatial inhomogeneity induces a static central peak with finite q width in the scattering cross section, accompanied by a dynamical component that is confined to the very vicinity of the disorder–induced phase transition.
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    Critical dynamics at incommensurate phase transitions and NMR relaxation experiments
    Kaufmann, B. A.; Schwabl, Franz; Täuber, Uwe C. (American Physical Society, 1999-05-01)
    We study the critical dynamics of crystals which undergo a second-order phase transition from a high-temperature normal phase to a structurally incommensurate (IC) modulated phase. We give a comprehensive description of the critical dynamics of such systems, e.g. valid for crystals of the A2BX4 family. Using an extended renormalization scheme, we present a framework in which we analyze the phases above and below the critical temperature TI . Above TI , the crossover from the critical behavior to the mean-field regime is studied. Specifically, the resulting width of the critical region is investigated. In the IC modulated phase, we consider explicitly the coupling of the order parameter modes to one-loop order. Here the Goldstone anomalies and their effect on measurable quantities are investigated. We show their relation with the postulated phason gap. While the theory can be applied to a variety of experiments, we concentrate on quadrupole-perturbed nuclear magnetic resonance (NMR) experiments. We find excellent agreement with these dynamical measurements and provide answers for some questions that arose from recent results.
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    Critical dynamics at incommensurate phase transitions and NMR relaxation experiments
    Kaufmann, B. A.; Schwabl, Franz; Täuber, Uwe C. (American Physical Society, 1999-05)
    We study the critical dynamics of crystals which undergo a second-order phase transition from a high-temperature normal phase to a structurally incommensurate (IC) modulated phase. We give a comprehensive description of the critical dynamics of such systems, e.g., valid for crystals of the A(2)BX(4) family. Using an extended renormalization scheme, we present a framework in which we analyze the phases above and below the critical temperature T-I. Above T-I, the crossover from the critical behavior to the mean-field regime is studied. Specifically, the resulting width of the critical region is investigated. In the IC modulated phase, we consider explicitly the coupling of the order parameter modes to one-loop order. Here the Goldstone anomalies and their effect on measurable quantities are investigated. We show their relation with the postulated phason gap. While the theory can be applied to a variety of experiments, we concentrate on quadrupole-perturbed nuclear magnetic resonance (NMR) experiments. We find excellent agreement with these dynamical measurements and provide answers for some questions that arose from recent results. [S0163-1829(99)03417-7].
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    Crossover from Isotropic to Directed Percolation
    Frey, E.; Täuber, Uwe C.; Schwabl, Franz (1994-06)
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    Crossover From Self-Similar to Self-Affine Structures in Precolation
    Frey, E.; Täuber, Uwe C.; Schwabl, Franz (Editions Physique, 1994-05-20)
    We study the crossover from self-similar scaling behavior to asymptotically self-affine (anisotropic) structures. As an example, we consider bond percolation with one preferred direction. Our theory is based on a field-theoretical representation, and takes advantage of a renormalization group approach designed for crossover phenomena. We calculate effective exponents for the connectivity describing the entire crossover region from isotropic to directed percolation, and predict at which scale of the anisotropy the crossover should occur. We emphasize the broad range of applicability of our method.
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    Defect-induced condensation and central peak at structural transitions
    Schwabl, Franz; Täuber, Uwe C. (1991-05-01)
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    Defect-induced condensation and the central peak at elastic phase transitions
    Bulenda, M.; Schwabl, Franz; Täuber, Uwe C. (1996-09-01)
    Static and dynamical properties of elastic phase transitions under the influence of short–range defects, which locally increase the transition temperature, are investigated. Our approach is based on a Ginzburg–Landau theory for three–dimensional crystals with one–, two– or three–dimensional soft sectors, respectively. Systems with a finite concentration nD of quenched, randomly placed defects display a phase transition at a temperature Tc(nD), which can be considerably above the transition temperature T0c of the pure system. The phonon correlation function is calculated in single–site approximation. For T > Tc(nD) a dynamical central peak appears; upon approaching Tc(nD), its height diverges and its width vanishes. Using an appropriate self–consistent method, we calculate the spatially inhomogeneous order parameter, the free energy and the specific heat, as well as the dynamical correlation function in the ordered phase. The dynamical central peak disappears again as the temperatur is lowered below Tc(nD). The inhomogeneous order parameter causes a static central peak in the scattering cross section, with a finite k width depending on the orientation of the external wave vector k relative to the soft sector. The jump in the specific heat at the transition temperatur of the pure system is smeared out by the influence of the defects, leading to a distinct maximum instead. In addition, there emerges a tiny discontinuity of the specific heat at Tc(nD). We also discuss the range of validity of the mean–field approach, and provide a more realistic estimate for the transition temperature.
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    Dimensional crossover in dipolar magnetic layers
    Bulenda, M.; Täuber, Uwe C.; Schwabl, Franz (IOP, 2000-01-14)
    We investigate the static critical behaviour of a uniaxial magnetic layer, with finite thickness L in one direction, yet infinitely extended in the remaining d dimensions. The magnetic dipole-dipole interaction is taken into account. We apply a variant of Wilson’s momentum shell renormalisation group approach to describe the crossover between the critical behaviour of the 3-D Ising, 2-d Ising, 3-D uniaxial dipolar, and the 2-d uniaxial dipolar universality classes. The corresponding renormalisation group fixed points are in addition to different effective dimensionalities characterised by distinct analytic structures of the propagator, and are consequently associated with varying upper critical dimensions. While the limiting cases can be discussed by means of dimensional ǫ expansions with respect to the appropriate upper critical dimensions, respectively, the crossover features must be addressed in terms of the renormalisation group flow trajectories at fixed dimensionality d.
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    Local condensation at elastic phase transitions
    Schwabl, Franz; Täuber, Uwe C. (1990)
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    Phase transitions: renormalization and scaling
    Schwabl, Franz; Täuber, Uwe C. (VCH, 1995)