scholarly journals Frozen quasi-long-range order in the random anisotropy Heisenberg magnet

2003 ◽  
Vol 68 (10) ◽  
Author(s):  
M. Itakura
Keyword(s):  
Long Range ◽  
Range Order ◽  
Long Range Order ◽  
Heisenberg Magnet ◽  
Random Anisotropy

scholarly journals QUASI-LONG RANGE ORDER IN GLASS STATES OF IMPURE LIQUID CRYSTALS, MAGNETS, AND SUPERCONDUCTORS

2001 ◽  
Vol 15 (22) ◽  
pp. 2945-2976 ◽  
Author(s):  
D. E. FELDMAN
Keyword(s):  
Liquid Crystals ◽  
Long Range ◽  
Disordered Systems ◽  
Critical Dimension ◽  
Range Order ◽  
Long Range Order ◽  
Weak Disorder ◽  
Random Anisotropy ◽  
Ordered Phases ◽  
Amorphous Magnets

We consider glass states of several disordered systems: vortices in impure superconductors, amorphous magnets, and nematic liquid crystals in random porous media. All these systems can be described by the random-field or random-anisotropy O(N) model. Even arbitrarily weak disorder destroys long range order in the O(N) model. We demonstrate that at weak disorder and low temperatures quasi-long range order emerges. In quasi-long-range-ordered phases the correlation length is infinite and correlation functions obey power dependencies on the distance. In pure systems quasi-long range order is possible only in the lower critical dimension and only in the case of Abelian symmetry. In the presence of disorder this type of ordering turns out to be more common. It exists in a range of dimensions and is not prohibited by non-Abelian symmetries.

Chemical Ordering and Microstructural Affects on Magnetic Properties of Sm2Fe17 and Sm2Fe17Nx

1999 ◽  
Vol 577 ◽  
Author(s):  
B.E. Meacham ◽  
K.W. Dennis ◽  
R.W. Mccallum ◽  
J.E. Shield
Keyword(s):  
Long Range ◽  
Domain Walls ◽  
Antiphase Domain ◽  
Small Degree ◽  
Range Order ◽  
Long Range Order ◽  
Chemical Order ◽  
Chemical Ordering ◽  
Random Anisotropy ◽  
Magnetic Hardness

ABSTRACTThe effect of chemical order and defect structure on the magnetization process in Sm2Fe17 and Sm2Fe17Nx has been investigated. In Sm2Fe17, chemical disorder results in the development of random anisotropy and a small degree of magnetic hardness. The anisotropy is reduced as long-range order increases. The motion of domain walls in Sm2Fe17Nx is more dependent on the antiphase domain structure than on the amount of long-range order.

scholarly journals Long range order in random anisotropy magnets

1990 ◽  
Vol 67 (9) ◽  
pp. 5778-5780 ◽  
Author(s):  
R. Fisch ◽  
A. B. Harris
Keyword(s):  
Long Range ◽  
Range Order ◽  
Long Range Order ◽  
Random Anisotropy

Superfluidity and Superconductivity

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Wave Packet ◽  
Long Range ◽  
Cooper Pair ◽  
Bose Condensation ◽  
Range Order ◽  
Condensed State ◽  
Long Range Order ◽  
Coherent Wave

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

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