Neutron Scattering by Ferroelectrics

Аксенов, В. Л.; Плакида, Н. М.; Stamenković, S.; Pontekorvo, D.B.

doi:10.1142/0331

Cited by 26 publications

(90 citation statements)

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“…It is easy to see that for a < bδ the minimum of the potential (1.5) is not unique and the system may undergo a displacement phase transition. For the case of so-called self-consistent phonon approximation [1], or for the displacement quantum spherical model it was proved in [48] for (1.3) and in [54,58] for (1.5). In general case this follows from [15], see also [47].…”

Section: Introductionmentioning

confidence: 99%

“…From the other side, another interesting phenomenon, the suppression of the long-range order by strong quantum fluctuations in such systems was experimentally observed (see, e.g. [55]) and was discussing long time ago from the physical point of view, see [51], or the books [1,19]. A rigorous study of this phenomenon was given in the series of papers.…”

Section: Introductionmentioning

confidence: 99%

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Gibbs state uniqueness for an anharmonic quantum crystal with a non-polynomial double-well potential

Rebenko¹,

Zagrebnov²

2006

J. Stat. Mech.

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We construct the Gibbs state for ν-dimensional quantum crystal with site displacements from IR d , d ≥ 1, and with a one-site non-polynomial double-well potential, which has harmonic asymptotic growth at infinity. We prove the uniqueness of the corresponding Euclidean Gibbs measure (EGM) in the lightmass regime for the crystal particles. The corresponding state is constructed via a cluster expansion technique for an arbitrary temperature T ≥ 0. We show that for all T ≥ 0 the Gibbs state (correlation functions) is analytic with respect to external field conjugated to displacements provided that the mass of particles m is less than a certain value m * > 0. The high temperature regime is also discussed.Keywords : quantum crystal model, Gibbs state, Euclidean Gibbs measures, quantum fluctuations, light-mass regime, cluster expansions. Mathematics Subject Classification : 60H30, 82B31 IntroductionIt is generally excepted that for investigation of different physical phenomena in quantum crystals one can consider an infinite system of interacting anharmonic oscillators, which are situated in the sites of ν-dimensional lattice Z Z ν . The heuristic Hamiltonian of such a system (in the case of 2-body interaction) has the following form:where m is the mass of particles, the operator ∆ j corresponds the kinetic energy of the system and, in fact, is d-dimensional Laplace operator in the one-particle Hilbert space, where dq is the Lebesgue measure onν is displacement of a particle from its position in the site j ∈ Z Z ν . For general case d ≤ ν ≥ 1. But the most of results, which where obtained earlier are for d = 1. The particles are confined near their sites by potential W (q j ). A harmonic one-site potential W harm (q j ) = 1 2 aq 2 j , a > 0 together with a harmonic two-particle interaction Q(·, ·) define a well-known harmonic crystal model (1.1). To produce a model describing a (ferroelectric) structural phase transition one usually takes for W (·) a doublewell anharmonic potential, keeping Q(·, ·) harmonic (see e.g. [1,19,24]). For example,or semibounded from below polynomials of higher degree with more than two equal minima. Here q 2 ≡ q · q is the scalar square of displacement vector q ∈ IR d . The proof of existence of phase transition in such kind of systems for harmonic interaction Q(q i , q j ) were obtained in [12,15,26,34,40,47,53] for the case2) whereQ = (Q ij ) i,j∈Z Z ν is a matrix of non-negative harmonic-force constants. The term h · q j = d α=1 h α q α j break the symmetry in the direction of the 1 external field h. The non-uniqueness of Gibbs states for h = 0 is proved when the mass of the particles m is sufficiently large and the temperature T is sufficiently low, or β = (kT ) −1 is sufficiently large. From the other side, another interesting phenomenon, the suppression of the long-range order by strong quantum fluctuations in such systems was experimentally observed (see, e.g. [55]) and was discussing long time ago from the physical point of view, see [51], or the books [1,19]. A rigorous stu...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gibbs state uniqueness for an anharmonic quantum crystal with a non-polynomial double-well potential

Rebenko¹,

Zagrebnov²

2006

J. Stat. Mech.

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“…It has been established [4][5][6][7][8][9][10][11][12][13][14][15][16]26,[46][47][48] that replacement of protons with deuterons significantly changes the transition temperatures, domain wall mobilities, thermal and dielectric properties of the crystals. These results indicate an importance of hydrogen bonds in the phase transitions in these types of crystals.…”

Section: Introductionmentioning

confidence: 99%

“…Attempts to describe experimental data for thermodynamic and dynamic characteristics of the KH 2 PO 4 type ferroelectrics and NH 4 H 2 PO 4 type antiferroelectrics have been made (see e. g. [4][5][6][7][8][9][10][11][12][13][14][15][16][97][98][99][100][101][102][103][104][105][106][107][108][109][110][111]). However, due to the neglected piezoelectric and short-range interactions, important in these compounds, the obtained there results (see [112][113][114]) cannot provide a proper qualitative, let alone quantitative, description of the experiment.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics and dynamical properties of the KH_{2}PO_{4} type ferroelectric compounds. A unified model

Levitskii¹,

Zachek²,

Vdovych³

et al. 2009

Condens. Matter Phys.

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Within the framework of the proposed unified proton ordering model for the ferroelectric compounds of the KH 2 PO 4 family, in the four-particle cluster approximation for the short-range interactions and mean field approximation for the long-range interactions, we calculate thermodynamic and longitudinal dynamic characteristics of the KD 2 PO 4 type ferroelectrics and ND 4 D 2 PO 4 type antiferroelectrics. Calculations for partially deuterated K(H 1−x Dx) 2 PO 4 type ferroelectrics and N(H 1−x Dx) 4 (H 1−x Dx) 2 PO 4 type antiferroelectrics are performed within the mean crystal approximation. It is shown that at the proper choice of the theory parameters, a good quantitative description of experimental data for the KH 2 PO 4 family crystals is obtained.

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“…In the vicinity of structural phase transitions (e.g., ferroelectric transitions [13] or martensitic transformations in metals [6,14]) this potential normally has several minima corresponding to several competing phases, the height of the barrier being much smaller than a typical cohesion energy. It is not surprising that the harmonic approximation is an extremally poor starting point to describe this situation.…”

Section: Introductionmentioning

confidence: 99%