Physical review. B, Condensed matter

Sound attenuation and dispersion in a diluted Ising model

A. Pawlak, B. Fechner

Published Nov 1, 1989• 15 citations

Abstract

The critical behavior of sound attenuation and dispersion in a diluted Ising system with a nonconserved order parameter is studied above ${T}_{c}$. The dynamical scaling functions are computed by the \ensuremath{\epsilon}-expansion method up to the first order.

DOI: 10.1103/physrevb.40.9324

Related papers

Propagation of ultrasound near the phase transition in Ising systems

A. Pawlak

Journal of Physics Condensed MatterOct 30, 198912 citations

Critical sound attenuation of three-dimensional Ising systems

Pavel Vladimirovich Prudnikov, Vladimir V. Prudnikov

Condensed Matter PhysicsJan 1, 20061 citation

Critical behaviors of the sound attenuation in a spin-1 Ising model

Mustafa Keskín, Rıza Erdem

The Journal of Chemical PhysicsMar 20, 200320 citations

High-Frequency Sound Attenuation and Dispersion in the Critical Region

Kyozi Kawasaki

Physical Review AMar 1, 197119 citations

The influence of disorder on the critical sound attenuation in solids

Pavel Vladimirovich Prudnikov, Vladimir V. Prudnikov

arXiv:cond-mat/0512316Journal of Physics Condensed MatterNov 1, 20054 citations

Critical properties of a dilute Ising model in the percolation limit

J. Heinrichs

Physical review. B, Condensed matterAug 1, 19781 citation

Physical review. B, Condensed matter

Sound attenuation and dispersion in a diluted Ising model

A. Pawlak, B. Fechner

Published Nov 1, 1989• 15 citations

Publisher

Abstract

The critical behavior of sound attenuation and dispersion in a diluted Ising system with a nonconserved order parameter is studied above

{T}_{c}

. The dynamical scaling functions are computed by the \ensuremath{\epsilon}-expansion method up to the first order.

DOI: 10.1103/physrevb.40.9324

Related papers

Propagation of ultrasound near the phase transition in Ising systems

A. Pawlak

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.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.

Journal of Physics Condensed MatterOct 30, 198912 citations

Critical sound attenuation of three-dimensional Ising systems

Pavel Vladimirovich Prudnikov, Vladimir V. Prudnikov

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 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.

Condensed Matter PhysicsJan 1, 20061 citation

Critical behaviors of the sound attenuation in a spin-1 Ising model

Mustafa Keskín, Rıza Erdem

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).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 Journal of Chemical PhysicsMar 20, 200320 citations

High-Frequency Sound Attenuation and Dispersion in the Critical Region

Kyozi Kawasaki

A general theory is presented for sound attenuation and dispersion near the critical point in the region of frequencies which are much greater than the characteristic frequency of order-parameter dynamics, but are much smaller than the frequency of sound with the wavelength equal to the range of correlation of local order-parameter fluctuations. The method used is the most general version of the mode-mode coupling theory plus the static and dynamic scaling hypotheses and some general properties of time-correlation functions. If we ignore the small critical exponent $\ensuremath{\alpha}$ associated with the heat-capacity singularity, we find that the attenuation behaves as $f{\ensuremath{\epsilon}}^{0}$ and the dispersion (relative sound-velocity change with frequency) as ${f}^{0}{\ensuremath{\epsilon}}^{0}$, where $f$ is the dimensionless frequency and $\ensuremath{\epsilon}$ the dimensionless temperature distance from the critical point.A general theory is presented for sound attenuation and dispersion near the critical point in the region of frequencies which are much greater than the characteristic frequency of order-parameter dynamics, but are much smaller than the frequency of sound with the wavelength equal to the range of correlation of local order-parameter fluctuations. The method used is the most general version of the mode-mode coupling theory plus the static and dynamic scaling hypotheses and some general properties of time-correlation functions. If we ignore the small critical exponent $\ensuremath{\alpha}$ associated with the heat-capacity singularity, we find that the attenuation behaves as $f{\ensuremath{\epsilon}}^{0}$ and the dispersion (relative sound-velocity change with frequency) as ${f}^{0}{\ensuremath{\epsilon}}^{0}$, where $f$ is the dimensionless frequency and $\ensuremath{\epsilon}$ the dimensionless temperature distance from the critical point.

Physical Review AMar 1, 197119 citations

The influence of disorder on the critical sound attenuation in solids

Pavel Vladimirovich Prudnikov, Vladimir V. Prudnikov

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 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.

arXiv:cond-mat/0512316Journal of Physics Condensed MatterNov 1, 20054 citations

Critical properties of a dilute Ising model in the percolation limit

J. Heinrichs

The critical behavior of the dilute Ising model on a Bethe lattice of coordination $z$ is studied in the percolation limit ($T\ensuremath{\rightarrow}0$) by means of a new moment-expansion procedure. Exact numerical results for the magnetization as a function of magnetic field at the critical concentration, $p={p}_{c}$ , are presented for $z=3$ and $z=4$ . In particular, the critical exponent ${\ensuremath{\delta}}_{P}$ is expected to agree well for very low fields with the approximate value ${\ensuremath{\delta}}_{P}=2$ obtained by Essam et al. The nature of deviations from the value ${\ensuremath{\delta}}_{P}=2$ is discussed and their consequences are noted. The case $p\ensuremath{\ne}{p}_{c}$ is also discussed.The critical behavior of the dilute Ising model on a Bethe lattice of coordination $z$ is studied in the percolation limit ($T\ensuremath{\rightarrow}0$) by means of a new moment-expansion procedure. Exact numerical results for the magnetization as a function of magnetic field at the critical concentration, $p={p}_{c}$, are presented for $z=3$ and $z=4$. In particular, the critical exponent ${\ensuremath{\delta}}_{P}$ is expected to agree well for very low fields with the approximate value ${\ensuremath{\delta}}_{P}=2$ obtained by Essam et al. The nature of deviations from the value ${\ensuremath{\delta}}_{P}=2$ is discussed and their consequences are noted. The case $p\ensuremath{\ne}{p}_{c}$ is also discussed.

Physical review. B, Condensed matterAug 1, 19781 citation

The critical behavior of sound attenuation and dispersion in a diluted Ising system with a nonconserved order parameter is studied above

{T}_{c}

. The dynamical scaling functions are computed by the \ensuremath{\epsilon}-expansion method up to the first order.

f

is the dimensionless frequency and $\ensuremath{\epsilon}$ the dimensionless temperature distance from the critical point.

The critical behavior of the dilute Ising model on a Bethe lattice of coordination

z

is studied in the percolation limit ($T\ensuremath{\rightarrow}0$) by means of a new moment-expansion procedure. Exact numerical results for the magnetization as a function of magnetic field at the critical concentration,

p={p}_{c}

, are presented for

z=3

and

z=4

. In particular, the critical exponent ${\ensuremath{\delta}}_{P}$ is expected to agree well for very low fields with the approximate value ${\ensuremath{\delta}}_{P}=2$ obtained by Essam et al. The nature of deviations from the value ${\ensuremath{\delta}}_{P}=2$ is discussed and their consequences are noted. The case $p\ensuremath{\ne}{p}_{c}$ is also discussed.