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arXiv:cond-mat/0512316 · Journal of Physics Condensed Matter

The influence of disorder on the critical sound attenuation in solids

Pavel Vladimirovich Prudnikov, Vladimir V. Prudnikov

Published Nov 1, 2005• 4 citations
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Abstract

The field-theoretic description of dynamical critical effects of the influence of disorder on acoustic anomalies near the temperature of the second-order phase transition is considered for three-dimensional Ising-like systems. Calculations of the sound attenuation in pure and dilute Ising-like systems near the critical point are presented. The dynamical scaling function for the critical attenuation coefficient is calculated. The influence of quenched disorder on the asymptotic behaviour of the critical ultrasonic anomalies is discussed.

DOI
10.1088/0953-8984/17/46/l01

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The field-theoretic description of dynamical critical effects of the influence of disorder on acoustic anomalies near the temperature of the second-order phase transition is considered for three-dimensional Ising-like systems. Calculations of the sound attenuation in pure and dilute Ising-like systems near the critical point are presented. The dynamical scaling function for the critical attenuation coefficient is calculated. The influence of quenched disorder on the asymptotic behaviour of the critical ultrasonic anomalies is discussed.
The field-theoretic description of dynamic critical effects of the disorder on acoustic anomalies near the temperature of second-order phase transition is considered for three-dimensional Ising-like systems.The calculations of sound attenuation in high temperature phase for pure and diluted Ising-like systems near the critical point are presented.The dynamic scaling function for critical attenuation coefficient is calculated.The effect of the quenched disorder on asymptotic behaviour of the critical ultrasonic anomalies is discussed.
The effect of long-range correlated quenched structural defects on the critical ultrasound attenuation and sound velocity dispersion is studied for three-dimensional Ising-like systems. A field-theoretical description of the dynamic critical effects of ultrasound propagation in solids is performed with allowance for both fluctuation and relaxation attenuation mechanisms. The temperature and frequency dependences of the dynamical scaling functions of the ultrasound critical characteristics are calculated in a two-loop approximation for different values of the correlation parameter aaa of the Weinrib-Halperin model with long-range correlated defects. The asymptotic behavior of the dynamical scaling functions in hydrodynamic and critical regions is separated. The influence of long-range correlated disorder on the asymptotic behavior of the critical ultrasonic anomalies is discussed.
The effects of order-parameter strain coupling on the critical (tricritical) sound attenuation and dispersion are studied above T c in the elastically isotropic Ising model. Under free boundary conditions a cross-over in the behaviour of acoustic quantities to a 'strong-coupling' regime is predicted. New scaling relations for the critical attenuation and dispersion are obtained and the corresponding scaling functions are calculated using an ε-expansion. Non-asymptotic effects are also discussed.
Theoretical ideas for deriving singularities of thermodynamical functions at the second-order phase transitions in spin systems with weak quenched disorder are considered. In particular, p-component vector magnets and the two-dimensional Ising model with disorder in spin-spin interactions are studied. Generalisation of the traditional renormalisation-group scheme, which takes into account non-perturbative spin-glass degrees of freedom, is proposed. Low-temperature properties and the phase transition in the Ising systems with quenched random fields are also considered.
Critical behaviors of the sound attenuation in a spin-1 Ising system with bilinear (J) and biquadratic (K) interactions are investigated within the framework of cluster variation method and Onsager theory of irreversible thermodynamics. The sound wave is assumed to couple mainly to the order parameter fluctuations which decay via order parameter relaxation processes. Two relaxation times are obtained and an expression is found for the sound attenuation coefficient (α) in terms of these relaxation times. The temperature behavior of the sound attenuation near the phase transition temperatures (Tc) is analyzed according to various values of Onsager coefficients (γij) and sound frequency (ω). For T<Tc it is found that the maxima of the attenuation shifted to lower temperatures with increasing ω and γij (i≠j) values. For T>Tc the data give evidence that there is no relaxational contribution to sound attenuation coming from order parameter fluctuations. On the other hand, a convergence is found in attenuation just below the critical and the tricritical points as (Tc−T), while a jump-discontinuity is observed for the first-order behavior. The frequency variation of the sound attenuation is also investigated and in addition to ω2-attenuation dependence observed in the hydrodynamic regime it is observed that in the high frequency region the attenuation is independent of ω and the ratio of two interaction parameters (J/K).
The critical behavior of sound attenuation and dispersion in a diluted Ising system with a nonconserved order parameter is studied above Tc{T}_{c}Tc​. The dynamical scaling functions are computed by the \ensuremath{\epsilon}-expansion method up to the first order.