Unusual long-range-order property of the Ising model on the Sierpiński gasket

1985 ◽  
Vol 32 (9) ◽  
pp. 5804-5806 ◽  
Author(s):  
S. H. Liu
Keyword(s):  
Ising Model ◽  
Long Range ◽  
Sierpinski Gasket ◽  
Range Order ◽  
Order Property ◽  
Long Range Order ◽  
Sierpiński Gasket

Transition to long-range order in the three-dimensional random-field Ising model

1991 ◽  
Vol 66 (25) ◽  
pp. 3281-3284 ◽  
Author(s):  
J. P. Hill ◽  
T. R. Thurston ◽  
R. W. Erwin ◽  
M. J. Ramstad ◽  
R. J. Birgeneau
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Long Range ◽  
Three Dimensional ◽  
Range Order ◽  
Long Range Order ◽  
Random Field Ising Model

ISING MODEL WITH STRONGLY CORRELATED RANDOM FIELDS

1988 ◽  
Vol 02 (10) ◽  
pp. 1137-1141 ◽  
Author(s):  
T. HORIGUCHI ◽  
L.L. GONCALVES
Keyword(s):  
Ising Model ◽  
Domain Wall ◽  
Long Range ◽  
Random Fields ◽  
Linear Chain ◽  
Ising Models ◽  
Range Order ◽  
Square Lattice ◽  
Long Range Order ◽  
Strongly Correlated

We investigate the Ising models with strongly correlated random fields, taking the values ±h0 and 0, on the square lattice and on the linear chain. The models present long range order and these results are consistent with the lower critical dimensionality obtained by the domain wall argument.

Loss of long range order in the 3D random field Ising model

1993 ◽  
Vol 70 (23) ◽  
pp. 3655-3658 ◽  
Author(s):  
J. P. Hill ◽  
Q. Feng ◽  
R. J. Birgeneau ◽  
T. R. Thurston
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Long Range ◽  
Range Order ◽  
Long Range Order ◽  
Random Field Ising Model

scholarly journals Long-range order in gravity

2019 ◽  
Vol 28 (08) ◽  
pp. 1950099 ◽  
Author(s):  
Giorgio Papini
Keyword(s):  
Ising Model ◽  
Long Range ◽  
Correlation Length ◽  
Dispersion Relations ◽  
Range Order ◽  
Long Range Order ◽  
Identical Particles ◽  
One Dimensional ◽  
Astrophysical Objects

Gravity-induced condensation takes the form of momentum alignment in an ensemble of identical particles. Use is made of a one-dimensional Ising model to calculate the alignment per particle and the correlation length as a function of the temperature. These parameters indicate that momentum alignment is possible in the proximity of some astrophysical objects and in Earth, or near Earth laboratories. Momenta oscillations behave as known spin oscillations and obey identical dispersion relations.

scholarly journals Instability of long-range order in a d = 3 random-field Ising model system: Fe xZn1-xF2

2000 ◽  
Vol 30 (4) ◽  
pp. 758-761 ◽  
Author(s):  
F. C. Montenegro ◽  
K. A. Lima ◽  
M. S. Torikachvili ◽  
A. H. Lacerda
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Long Range ◽  
Model System ◽  
Range Order ◽  
Long Range Order ◽  
Random Field Ising Model

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.

Sign in / Sign up

Export Citation Format

Share Document