scholarly journals Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates

Soft Matter ◽  
2019 ◽  
Vol 15 (44) ◽  
pp. 9041-9055 ◽  
Author(s):  
E. E. Ferrero ◽  
E. A. Jagla
Keyword(s):  
Critical Exponents ◽  
Mean Field ◽  
Amorphous Solids ◽  
Stress Dependent ◽  
Local Yielding

Elastoplastic models are analyzed at the yielding transition. Universality and critical exponents are discussed. The flowcurve exponent happens to be sensitive to the local yielding rule. An alternative mean-field description of yielding is explained.

Nonclassical critical exponents out of mean-field results

1998 ◽  
Vol 260 (1-2) ◽  
pp. 99-105 ◽  
Author(s):  
Tânia Tomé ◽  
Mário J.de Oliveira
Keyword(s):  
Critical Exponents ◽  
Mean Field

scholarly journals Continuum limit of the vibrational properties of amorphous solids

2017 ◽  
Vol 114 (46) ◽  
pp. E9767-E9774 ◽  
Author(s):  
Hideyuki Mizuno ◽  
Hayato Shiba ◽  
Atsushi Ikeda
Keyword(s):  
Large Scale ◽  
Continuum Limit ◽  
Scaling Law ◽  
Mean Field ◽  
Low Frequency ◽  
Amorphous Solids ◽  
Mode Analysis ◽  
Vibrational Modes ◽  
Phonon Modes ◽  
The Continuum

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.

The Curie–Weiss–Néel model of a ferrimagnet

1981 ◽  
Vol 59 (7) ◽  
pp. 883-887 ◽  
Author(s):  
R. G. Bowers ◽  
S. L. Schofield
Keyword(s):  
Exact Solution ◽  
Critical Phenomena ◽  
Critical Exponents ◽  
Mean Field ◽  
The Other ◽  
New Model ◽  
Total Magnetization ◽  
Present Context ◽  
Elementary Methods ◽  
Parallel Fashion

An analogue, for ferrimagnetism, of the Curie–Weiss model ferromagnet is introduced. The resulting structure, the Curie–Weiss–Néel model, is based on a two sublattice description in which spins of one magnitude occupy one sublattice and spins of another magnitude occupy the other. Attention is concentrated on the case in which spins on the different sublattices tend to align in an anti-parallel fashion. Many properties of the new model are similar to those of the Curie–Weiss ferromagnet. Artificially long-ranged interactions connect spins on the different sublattices. The complete thermodynamics can be obtained exactly by relatively elementary methods. The exact solution of the model is essentially identical with the appropriate mean field results (of Néel). Attention is given to the Néel point and associated critical phenomena. Many standard critical exponents are calculated and, of course, classical exponent values result. Novel features of critical phenomena in ferrimagnets are considered. These are associated with the fact that, theoretically, the staggered magnetization and staggered fields are important while, experimentally, the total magnetization and uniform fields are usually employed. It is shown that, within the present context, corresponding staggered and uniform properties have identical exponent values.

scholarly journals Impact of jamming criticality on low-temperature anomalies in structural glasses

2019 ◽  
Vol 116 (28) ◽  
pp. 13768-13773 ◽  
Author(s):  
Silvio Franz ◽  
Thibaud Maimbourg ◽  
Giorgio Parisi ◽  
Antonello Scardicchio
Keyword(s):  
Low Temperature ◽  
Specific Heat ◽  
Field Model ◽  
Analytic Solution ◽  
Mean Field ◽  
Universality Class ◽  
Amorphous Solids ◽  
Anomalous Behavior ◽  
Marginal Stability ◽  
Mean Field Model

We present a mechanism for the anomalous behavior of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a cross-over temperature above which the specific heat scales linearly with temperature, while below it, a cubic scaling is displayed. This relies on two crucial features of the phase diagram: (i) the marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-law scaling; and (ii) the vicinity of the classical jamming critical point, as the cross-over temperature gets lowered when approaching it. This scenario arises from a direct study of the thermodynamics of the system in the quantum regime, where we show that, contrary to crystals, the Debye approximation does not hold.

scholarly journals Critical behavior of the spontaneous polarization and the dielectric susceptibility close to the cubic-tetragonal transition in BaTiO3

2015 ◽  
Vol 05 (03) ◽  
pp. 1550024
Author(s):  
H. Yurtseven ◽  
F. Oğuz
Keyword(s):  
Critical Behavior ◽  
Critical Exponents ◽  
Spontaneous Polarization ◽  
Field Model ◽  
Mean Field ◽  
Dielectric Susceptibility ◽  
Mean Field Model ◽  
Temperature And Pressure ◽  
Quantum Limits

Using Landau mean field model, the spontaneous polarization and the dielectric susceptibility are analyzed as functions of temperature and pressure close to the cubic–tetragonal (ferroelectric–paraelectric) transition in [Formula: see text]. From the analysis of the dielectric susceptibility and the spontaneous polarization, the critical exponents are deduced in the classical and quantum limits for [Formula: see text]. From the critical behavior of the dielectric susceptibility, the spontaneous polarization can be described for the ferroelectric–paraelectric (cubic to tetragonal) transition between 4 and 8 GPa at constant temperatures of 0 to 200 K in [Formula: see text] within the Landau mean field model given here.

scholarly journals Field-induced tricritical phenomenon and magnetic structures in magnetic Weyl semimetal candidate NdAlGe

2021 ◽  
Author(s):  
Jun Zhao ◽  
Wei Liu ◽  
Aziz Ur Rahman ◽  
Fanying Meng ◽  
Langsheng Ling ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Critical Exponents ◽  
Tricritical Point ◽  
Mean Field ◽  
Scaling Analysis ◽  
Topological Properties ◽  
Mean Field Model ◽  
Spin Configuration ◽  
Magnetic Structures ◽  
Weyl Semimetal

Abstract Non-centrosymmetric NdAlGe is considered to be a candidate for magnetic Weyl semimetal in which the Weyl nodes can be moved by magnetization. Clarification of the magnetic structures and couplings in this system is thus crucial to understand its magnetic topological properties. In this work, we conduct a systematical study of magnetic properties and critical behaviors of single-crystal NdAlGe. Angle-dependent magnetization exhibits strong magnetic anisotropy along the c-axis and absolute isotropy in the ab-plane. The study of critical behavior with H//c gives critical exponents β = 0.236(2), γ = 0.920(1), and δ = 4.966(1) at critical temperature TC = 5.2(2) K. Under the framework of the universality principle, M(T, H) curves are scaled into universality curves using these critical exponents, demonstrating reliability and self-consistency of the obtained exponents. The critical exponents of NdAlGe are close to the theoretical prediction of a tricritical mean-field model, indicating a field-induced tricritical behavior. Based on the scaling analysis, a H −T phase diagram for NdAlGe with H//c is constructed, revealing a ground state with an up-up- down spin configuration. The phase diagram unveils multiple phases including up-up-down domains, up-up-down ordering state, polarized ferromagnetic (PFM), and paramagnetic (PM) phases, with a tricritical point (TCP) located at the intersection [TT CP = 5.27(1) K, HT CP = 30.1(3) kOe] of up-up-down, PFM, and PM phases. The multiple phases and magnetic structures imply a delicate competition and balance between variable interactions and couplings, laying a solid foundation for unveiling topological properties and critical phenomena in this system.

scholarly journals Critical Site Percolation in High Dimension

2020 ◽  
Vol 181 (3) ◽  
pp. 816-853
Author(s):  
Markus Heydenreich ◽  
Kilian Matzke
Keyword(s):  
High Dimension ◽  
Critical Exponents ◽  
Mean Field ◽  
High Dimensions ◽  
Lace Expansion ◽  
Site Percolation ◽  
Triangle Condition ◽  
Hypercubic Lattice ◽  
Infra Red ◽  
Critical Site

Abstract We use the lace expansion to prove an infra-red bound for site percolation on the hypercubic lattice in high dimension. This implies the triangle condition and allows us to derive several critical exponents that characterize mean-field behavior in high dimensions.

scholarly journals Dynamical critical exponents for the mean-field Potts glass

2012 ◽  
Vol 85 (5) ◽  
Author(s):  
F. Caltagirone ◽  
G. Parisi ◽  
T. Rizzo
Keyword(s):  
Critical Exponents ◽  
Mean Field ◽  
The Mean
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