Spin Models for Ferroelastics: towards a Spin Glass Description of Strain Glass

2011 ◽  
Vol 172-174 ◽  
pp. 1078-1083 ◽  
Author(s):  
Romain Vasseur ◽  
Turab Lookman
Keyword(s):  
Mean Field ◽  
Three Dimensional ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Zero Field ◽  
High Symmetry ◽  
Spin Models ◽  
Wide Range ◽  
Long Range Interactions ◽  
Field Cooling

We review the description of ferroelastic transitions in terms of spin models. We show how one can systematically obtain a pseudo-spin Hamiltonian from the Landau energy describing the first order transition between Austenite/Martensite phases. It is shown that a Local Mean-field approximation predicts the same microstructure as the continuous Landau model in terms of strain variables. This method can be applied to a wide range of two and three dimensional transitions. We then demonstrate how quenched disorder in such pseudo-spin models yields the existence of a glass phase, characterized by the Edwards-Anderson order parameter. Our approach uses Mean-field approximation and Monte-Carlo simulations (using Zero Field Cooling/Field Cooling experiments) to study the influence of the long-range interactions. Although our model captures the salient features of a ferroelastic material in the presence of disorder, the influence of the disorder on the high symmetry austenite phase is not quite consistent with expected behavior. We examine different means of introducing disorder that can improve upon the results.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

scholarly journals The Possibility of Many Compensation Points in a Mixed-Spin Ising Ferrimagnetic System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hadey K. Mohamad
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
Spin Model ◽  
Mean Field Approximation ◽  
Zero Field ◽  
Mixed Spin ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
The Mean

The magnetic properties of a ferrimagnetic mixed spin-3/2 and spin-5/2 Ising model with different anisotropies are investigated by using the mean-field approximation (MFA). In particular, the effect of magnetic anisotropies on the compensation phenomenon, acting on A-atoms and B-ones for the mixed-spin model, has been considered in a zero field. The free energy of a mixed-spin Ising ferrimagnetic system from MFA of the Hamiltonian is calculated. By minimizing the free energy, we obtain the equilibrium magnetizations and the compensation points. The phase diagram of the system in the anisotropy dependence of transition temperature has been discussed as well. Our results of this model predict the existence of many (two or three) compensation points in the ordered system on a simple cubic lattice.

scholarly journals The Variational Reduction for Low-Dimensional Fermi Gases and Bose–Fermi Mixtures: A Brief Review

2019 ◽  
Vol 4 (1) ◽  
pp. 22
Author(s):  
Pablo Díaz ◽  
David Laroze ◽  
Boris Malomed
Keyword(s):  
Equations Of Motion ◽  
Mean Field ◽  
Three Dimensional ◽  
Field Approximation ◽  
Matter Wave ◽  
Mean Field Approximation ◽  
Degenerate Gases ◽  
Dynamical Regimes ◽  
Low Dimensional ◽  
Good Agreement

We present a summary of some recent theoretical results for matter-wave patterns in Fermi and Bose–Fermi degenerate gases, obtained in the framework of the quasi-mean-field approximation. We perform a dimensional reduction from the three-dimensional (3D) equations of motion to 2D and 1D effective equations. In both cases, comparison of the low-dimensional reductions to the full model is performed, showing very good agreement for ground-state solutions. Some complex dynamical regimes are reported too for the corresponding 1D systems.

Processus de branchement en champ moyen et réaction PCR

2001 ◽  
Vol 33 (2) ◽  
pp. 391-403 ◽  
Author(s):  
Didier Piau
Keyword(s):  
Branching Process ◽  
Random Number ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Process Mean ◽  
Dna Mutations ◽  
Wide Range ◽  
The Mean ◽  
Efficiency Rate

Sun and Waterman model DNA mutations during the PCR reaction by a non-canonical branching process. Mean-field approximated values fit the simulated values surprisingly well. We prove this as a theoretical result, for a wide range of the parameters. Thus, we bound explicitly the biases, in law and in the mean, that the mean-field approximation induces in the random number of mutations of a DNA molecule, as a function of the initial number of molecules, of the number of PCR cycles, of the efficiency rate and of the mutation rate. The range where we prove that the approximation is good contains the observed mutation rates in many actual PCR reactions.

Pressure and Temperature Effects in Homopolymer Blends and Diblock Copolymers

1997 ◽  
Vol 30 (5) ◽  
pp. 696-701 ◽  
Author(s):  
H. Frielinghaus ◽  
D. Schwahn ◽  
K. Mortensen ◽  
L. Willner ◽  
K. Almdal
Keyword(s):  
Interaction Parameter ◽  
Diblock Copolymers ◽  
Mean Field ◽  
Three Dimensional ◽  
Thermal Fluctuation ◽  
Thermal Fluctuations ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Phase Boundaries ◽  
Composition Fluctuations

Thermal composition fluctuations in a homogeneous binary polymer blend and in a diblock copolymer were measured by small-angle neutron scattering as a function of temperature and pressure. The experimental data were analyzed with theoretical expressions, including the important effect of thermal fluctuations. Phase boundaries, the Flory–Huggins interaction parameter and the Ginzburg number were obtained. The packing of the molecules changes with pressure. Therefore, the degree of thermal fluctuation as a function of packing and temperature was studied. While in polymer blends packing leads, in some respects, to a universal behaviour, such behaviour is not found in diblock copolymers. It is shown that the Ginzburg number decreases with pressure sensitively in blends, while it is constant in diblock copolymers. The Ginzburg number is an estimation of the transition between the universality classes of the `mean-field' approximation and the three-dimensional Ising model. The phase boundaries in blends increase with pressure, while the phase boundary of the studied block copolymer shows an unusual shape: with increasing pressure it first decreases and then increases. Its origin is an increase of the entropic and of the enthalpic parts, respectively, of the Flory–Huggins interaction parameter.

Interchain Interaction in Quasi-One-Dimension Organic Polymer Ferromagnets

1997 ◽  
Vol 11 (19) ◽  
pp. 821-827
Author(s):  
Hong-Tao Li
Keyword(s):  
Energy Gap ◽  
Mean Field ◽  
Three Dimensional ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Organic Polymer ◽  
Interchain Interaction ◽  
Energy Bands ◽  
Interchain Coupling ◽  
Organic Ferromagnets

A theoretical model is developed to describe quasi-one-dimensional organic ferromagnets after considering the interchain interaction as an interchain electron-transfer. By employing the mean-field approximation, four energy bands which exhibit three-dimensional anisotropic aspect are obtained. When the interchain coupling increases, the energy gap decreases. In the case of small dimerization order parameter, due to the interchain coupling, the band gap may disappear and the conjugated π-electrons in the main chain show ferromagnetic order in the ground state.

MEAN-FIELD THEORY FOR LAYERED HIGH-TEMPERATURE SUPERCONDUCTORS

1988 ◽  
Vol 02 (05) ◽  
pp. 1059-1065 ◽  
Author(s):  
D. Baeriswyl ◽  
T. Schneider
Keyword(s):  
High Temperature Superconductors ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional ◽  
Interlayer Coupling ◽  
Interlayer Spacing ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Pairing Mechanism ◽  
The Mean

Using the mean-field approximation we study a model for quasi-two-dimensional layered superconductors. The interlayer coupling, assumed to be mediated by a small electron hopping term, is found to leave Tc practically unaffected. Consequently, a three-dimensional pairing mechanism is required to explain the observed dependence of Tc on the average interlayer spacing in the Bi and Tl compounds.

scholarly journals On Magnetic Inhibition of Thermal Convection

1972 ◽  
Vol 25 (6) ◽  
pp. 703 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy ◽  
EA Spiegel
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Quantitative Estimates ◽  
Wide Range ◽  
The Face ◽  
The Mean ◽  
The Magnetic Field

The effect of an imposed vertical magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. Solutions are found over a wide range of conditions, for free boundaries, by a combination of numerical and analytic techniques. Quantitative estimates are made of the significant modifications to the heat transfer which are brought about by the presence of the magnetic field. It is found that the general properties of nonlinear steady cellular convection seem to persist in the face of magnetic inhibition.

Influence of Ti Substitution on the Critical Properties of CuxCryTizSe4 (z = 0.24 and 0.35)

2012 ◽  
Vol 194 ◽  
pp. 144-147 ◽  
Author(s):  
Józef Krok-Kowalski ◽  
Grzegorz Władarz ◽  
Paweł Rduch ◽  
Ewa Malicka ◽  
Tadeusz Groń ◽  
...  
Keyword(s):  
Mean Field ◽  
Theoretical Models ◽  
Zero Field ◽  
Critical Properties ◽  
Spin Frustration ◽  
Mean Field Model ◽  
Long Range Interactions ◽  
The Mean ◽  
Ti Substitution ◽  
Field Cooling

Magnetization, M, and susceptibility, , measurements of CuxCryTizSe4 (z = 0.24 and 0.35) showed both strong lowering of magnetic moment in comparison with CuCr2Se4 matrix and zero-field-cooling (ZFC) – field-cooling (FC) susceptibility splitting characteristic for the spin-glass (SG) behaviour. Isothermal magnetization curves, M(H), easy saturate and large both the Curie (TC ~ 250 K) and Curie-Weiss (θCW ~ 280 K) temperatures indicate the ferromagnetic order which coexists with the SG state. The critical behaviour of polycrystalline CuxCryTizSe4 spinels investigated around the paramagnetic–ferromagnetic (PM-FM) phase transition revealed that the values of critical exponents are close to those predicted by the mean field model for long-range interactions only for Cu1.02Cr1.77Ti0.24Se4. It means that the larger spin frustration the more difficulty is it to describe the critical properties with the aid of the theoretical models.

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