scholarly journals Посвящается памяти А.И. Морозова Фаза Имри-Ма в системах с дефектами типа "случайное локальное поле" и "случайная локальная анизотропия" (О б з о р)

2022 ◽  
Vol 64 (1) ◽  
pp. 3
Author(s):  
А.А. Берзин ◽  
А.И. Морозов ◽  
А.С. Сигов
Keyword(s):  
Random Field ◽  
Crystallite Size ◽  
Local Field ◽  
Random Fields ◽  
Coercive Field ◽  
Order Parameter ◽  
Large Scale ◽  
Long Range Order ◽  
Local Anisotropy ◽  
Random Anisotropy

The conditions for the appearance in systems with defects of the "random local field" and "random local anisotropy" type of the Imry-Ma phases, in which the direction of the order parameter follows large-scale fluctuations of a random field or random anisotropy, are considered. It is shown that the anisotropy of the distribution of random fields of defects in the space of the order parameter can lead to the appearance of the long-range order. An attention is paid to phase diagrams arising as a result of competition between random fields of defects and anisotropy induced by defects. By the example of a system with random anisotropy (nanocrystalline ferromagnet), the dependences of the coercive field on the crystallite size are considered.

scholarly journals Дальний порядок в двумерных O(n)-моделях, индуцированный случайными полями, и состояние Имри-Ма

2020 ◽  
Vol 62 (2) ◽  
pp. 281
Author(s):  
А.А. Берзин ◽  
А.И. Морозов ◽  
А.С. Сигов
Keyword(s):  
Phase Transition ◽  
Local Field ◽  
Random Fields ◽  
Order Parameter ◽  
Smooth Transition ◽  
Two Dimensional ◽  
Strong Anisotropy ◽  
Continuous Symmetry ◽  
Weak Anisotropy ◽  
Ordered State

A.A. Berzin, A.I. Morosov, and A.S. Sigov The influence of defects of the “random local field” type with an anisotropic distribution of random fields on two-dimensional models with continuous symmetry of the vector order parameter is considered. In the case of weak anisotropy of random fields, with decreasing temperature there takes place a smooth transition from the paramagnetic phase with dynamic fluctuations of the order parameter to the Imry-Ma phase with static fluctuations caused by fluctuations of the random field of defects. In the case of strong anisotropy of random fields, defects lead to an effective decrease in the number of components of the order parameter and the appearance of a phase transition to an ordered state at finite temperature.

A rigorous multiscale random field approach to generate large scale rough rock surfaces

2021 ◽  
Vol 142 ◽  
pp. 104716
Author(s):  
M. Jeffery ◽  
J. Huang ◽  
S. Fityus ◽  
A. Giacomini ◽  
O. Buzzi
Keyword(s):  
Random Field ◽  
Large Scale ◽  
Field Approach

scholarly journals Functional Brain Connectivity Revealed by Sparse Coding of Large-Scale Local Field Potential Dynamics

2018 ◽  
Vol 32 (2) ◽  
pp. 255-270 ◽  
Author(s):  
Han Wang ◽  
Kun Xie ◽  
Li Xie ◽  
Xiang Li ◽  
Meng Li ◽  
...  
Keyword(s):  
Local Field ◽  
Sparse Coding ◽  
Local Field Potential ◽  
Large Scale ◽  
Brain Connectivity ◽  
Field Potential ◽  
Functional Brain

scholarly journals Identification and isotropy characterization of deformed random fields through excursion sets

2018 ◽  
Vol 50 (3) ◽  
pp. 706-725
Author(s):  
Julie Fournier
Keyword(s):  
Random Field ◽  
Euler Characteristic ◽  
Random Fields ◽  
Weak Form ◽  
Invariance Property ◽  
Basic Domain ◽  
Excursion Sets ◽  
The Mean ◽  
Isotropic Random

Abstract A deterministic application θ:ℝ2→ℝ2 deforms bijectively and regularly the plane and allows the construction of a deformed random field X∘θ:ℝ2→ℝ from a regular, stationary, and isotropic random field X:ℝ2→ℝ. The deformed field X∘θ is, in general, not isotropic (and not even stationary), however, we provide an explicit characterization of the deformations θ that preserve the isotropy. Further assuming that X is Gaussian, we introduce a weak form of isotropy of the field X∘θ, defined by an invariance property of the mean Euler characteristic of some of its excursion sets. We prove that deformed fields satisfying this property are strictly isotropic. In addition, we are able to identify θ, assuming that the mean Euler characteristic of excursion sets of X∘θ over some basic domain is known.

scholarly journals Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

2017 ◽  
Vol 54 (3) ◽  
pp. 833-851 ◽  
Author(s):  
Anders Rønn-Nielsen ◽  
Eva B. Vedel Jensen
Keyword(s):  
Random Field ◽  
Large Class ◽  
Random Fields ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Excursion Sets ◽  
Excursion Set ◽  
Fixed Radius ◽  
Asymptotic Probability ◽  
The Right

Abstract We consider a continuous, infinitely divisible random field in ℝd, d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields, we compute the asymptotic probability that the excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

The temperature dependence of the long-range order parameter of Ni3Al

1977 ◽  
Vol 10 (1) ◽  
pp. 14-17 ◽  
Author(s):  
D. P. Pope ◽  
J. L. Garin
Keyword(s):  
Long Range ◽  
Order Parameter ◽  
Anomalous Behavior ◽  
Range Order ◽  
Range Order Parameter ◽  
Long Range Order ◽  
Temperature Range ◽  
Ordered Alloys ◽  
Fine Particle Size ◽  
Increasing Temperature

The macroscopic yield stress of Ni3Al increases rapidly with temperature, reaching a maximum at about 700°C. Such anomalous behavior has been observed in other ordered alloys which undergo partial disordering with increasing temperature, e.g. Cu3Au. The long-range order parameter, S, of stoichiometric Ni3Al powder was measured over the temperature range 25°C to 1000°C and great care was taken to ensure a fine particle size and thus avoid extinction effects. The results of this study showed that, in Ni3Al, S remains constant at about 0.93 over the entire temperature range investigated. This means that theories relating the strength of ordered alloys to S are not applicable to Ni3Al.

The Effect of Growth Temperature and Substrate Misorientation on Degree of Order and Antiphase Domain Size in Ga0.52In0.48P Epilayers Grown on GaAs (001) Substrates by Gs-Mbe

1998 ◽  
Vol 523 ◽  
Author(s):  
C. Meenakarn ◽  
A. E. Staton-bevan ◽  
S. P. Najda ◽  
G. Duggan ◽  
A. H. Kean
Keyword(s):  
Band Gap ◽  
Long Range ◽  
Growth Temperature ◽  
Order Parameter ◽  
Plate Thickness ◽  
Antiphase Domain ◽  
Range Order ◽  
Range Order Parameter ◽  
Long Range Order ◽  
Gaas Substrates

AbstractA Transmission Electron Microscopy (TEM), Photoluminescence (PL) and Photoluminescence Excitation Spectroscopy (PLE) investigation has been conducted on Ga0.52In0.48P epilayers grown on (001) GaAs substrates by Gas-Source Molecular Beam Epitaxy.For Ga0.52In0.48P epilayers grown on exact (001) GaAs substrates, increasing the growth temperature from 480°C to 535°C increased the antiphase domain plate thickness, t, from 7.3±0.4 to 17.4±0.9 Å, and decreased the long range order parameter, n, from 0.32 to 0.18±0.1. For epilayers grown at 530°C, on GaAs(001) substrates off-cut 0°, 7°, 10° and 15° towards [111]A, increasing the substrate misorientation from 0° to 15° decreased the antiphase domain plate thickness, from 12.3±0.6 to 6.0±0.3 Å. The long range order parameter also decreased from 0.19 to 0.10±0.01.The band gap energies of these samples, grown by GS-MBE, were close to those reported for fully disordered Ga0.52In0.48P epilayers grown by MOCVD at ∼760°C. This shows that GSMBE is also a good technique to grow GaInP for high band gap optical data storage applications and at lower growth temperatures. The optimum growth conditions in this study were at a growth temperature of 530°C on (001) GaAs substrate with 15° off-cut towards [111]A.

Pb()O3-type Perovskites: Part I. Pair-correlation Theory of Order-disorder Phase Transition

1997 ◽  
Vol 12 (8) ◽  
pp. 2117-2126 ◽  
Author(s):  
Hyun M. Jang ◽  
Su-Chan Kim
Keyword(s):  
Long Range ◽  
Order Parameter ◽  
Short Range ◽  
Short Range Order ◽  
Pair Correlation ◽  
Range Order ◽  
Statistical Thermodynamic ◽  
Range Order Parameter ◽  
Long Range Order ◽  
Short Range Order Parameter

The limitation of the long-range order parameter and the necessity of the short-range order parameter for the thermodynamic description of Pb()O3-type perovskites are discussed. Based on the discussion, a statistical thermodynamic model that takes into account the configuration of the neighboring B-site ions (B′ and B″ cations) was developed. A pair-correlation approximation was used in the calculation of the configurational entropy and the long-range coulombic interaction energy between the nearest B-site ions. The theoretical calculations using Pb(Sc1/2Ta1/2)O3 (PST) and Pb(Sc1/2Nb1/2)O3 (PSN) systems indicate that the short-range order parameter persists over a wide range of temperatures examined (0–1800 K) and that there possibly occur consecutive long-range order-disorder transitions in the configuration of B-site cations. The possibility of the existence of short-range ordering above the long-range order-disorder transition temperature was also examined using the annealed PSN specimen as a typical example of Pb()O3-type perovskites.

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