Relaxation Dynamics of Disordered Ising Model. Two-Site Cluster Approximation

Levitskii,; Sorokov,; Sokolovskii,

doi:10.5488/cmp.7.117

Cited by 3 publications

(4 citation statements)

References 12 publications

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“…The true parameters of the Hamiltonian (2.1) are κ iα , K iα,jβ . Since long range interactions can be taken into account in the mean field approximation (these simply lead to the emerging of effective field term in the fields κ iα ) [2,3] here we suppose the pair interactions to be short-range…”

Section: The Model and The Approachmentioning

confidence: 99%

“…iα (ω)/δκ jβ (ω) [3]. In figure 1 the results of the theory are compared with dielectric measurements for Cs(H 1−x D x ) 2 PO 4 crystals [7,8].…”

Section: Formulating a Two-site Cluster Approximationmentioning

confidence: 99%

“…The dynamic pair CF of the model in such an approach can be expressed via dynamic pair CFs of Ising model (the derivation is similar to that given in the appendix in [3]) M (2) ++ ( q, ω)M…”

Section: Mitsui Modelmentioning

confidence: 99%

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Relaxation Dynamics of Disordered Ising-Like Models

Levitskii¹,

Sokolovskii²

1999

Condens. Matter Phys.

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Section: The Model and The Approachmentioning

confidence: 99%

“…iα (ω)/δκ jβ (ω) [3]. In figure 1 the results of the theory are compared with dielectric measurements for Cs(H 1−x D x ) 2 PO 4 crystals [7,8].…”

Section: Formulating a Two-site Cluster Approximationmentioning

confidence: 99%

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Relaxation Dynamics of Disordered Ising-Like Models

Levitskii¹,

Sokolovskii²

1999

Condens. Matter Phys.

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“…In such a way a problem of the calculation of dynamic properties of the disordered Ising model arises. Papers [49][50][51][52] treat the Glauberian dynamics of the model within the twosite cluster approximation. NSO dynamics of the disordered Ising model is an open problem.…”

Section: Dynamics and Thermodynamics Of Deuterated Quasi-1d Ferroelecmentioning

confidence: 99%

To the Theory of Relaxation Phenomena in Quasi-One-Dimensional Ferroelectrics With Hydrogen Bonds. Nonequilibrium Statistical Operator Approach

Levitskii¹,

Zachek²,

Sokolovskii³

1998

Condens. Matter Phys.

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Kinetic equations for the dielectric properties of CsH 2 PO 4 -type ferroelectrics are derived within the nonequilibrium statistical operator method proposed by D.N.Zubarev. These equations are solved with two different approaches. In the first approach the closure relation in the spirit of a two-site cluster approximation is used. In the second approach the exact relation between the static correlation functions is extrapolated to a dynamic case and used as a closure relation. The both approaches give similar results. The obtained dynamic characteristics are close to those of the Glauber model and are shown to describe the dynamic dielectric permittivity of CsH 2 PO 4 and CsD 2 PO 4 crystals.

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Model fluid in a porous medium: Results for a Bethe lattice

2003

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We consider a lattice gas with quenched impurities or "quenched-annealed binary mixture" on the Bethe lattice. The quenched part represents a porous matrix in which the (annealed) lattice gas resides. This model features the three main factors of fluids in random porous media: wetting, randomness, and confinement. The recursive character of the Bethe lattice enables an exact treatment, whose key ingredient is an integral equation yielding the one-particle effective field distribution. Our analysis shows that this distribution consists of two essentially different parts. The first one is a continuous spectrum and corresponds to the macroscopic volume accessible to the fluid, the second is discrete and comes from finite closed cavities in the porous medium. Those closed cavities are in equilibrium with the bulk fluid within the grand canonical ensemble we use, but are inaccessible in real experimental situations. Fortunately, we are able to isolate their contributions. Separation of the discrete spectrum facilitates also the numerical solution of the main equation. The numerical calculations show that the continuous spectrum becomes more and more rough as the temperature decreases, and this limits the accuracy of the solution at low temperatures.

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Relaxation Dynamics of Disordered Ising Model. Two-Site Cluster Approximation

Cited by 3 publications

References 12 publications

Relaxation Dynamics of Disordered Ising-Like Models

Relaxation Dynamics of Disordered Ising-Like Models

To the Theory of Relaxation Phenomena in Quasi-One-Dimensional Ferroelectrics With Hydrogen Bonds. Nonequilibrium Statistical Operator Approach

Model fluid in a porous medium: Results for a Bethe lattice

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