Evidence for long-range order in the Heisenberg antiferromagnet on a triangular lattice

1990 ◽  
Vol 42 (13) ◽  
pp. 8638-8639 ◽  
Author(s):  
G. B. Arnold ◽  
G. J. Mata
Keyword(s):  
Long Range ◽  
Triangular Lattice ◽  
Range Order ◽  
Long Range Order ◽  
Heisenberg Antiferromagnet

ORDERING PROBLEM FOR THE ANTIFERROMAGNETIC POTTS MODEL: T=0 MONTE-CARLO STUDIES

1991 ◽  
Vol 05 (19) ◽  
pp. 3061-3071 ◽  
Author(s):  
A.V. BAKAEV ◽  
V.I. KABANOVICH ◽  
A.M. KURBATOV
Keyword(s):  
Monte Carlo ◽  
Long Range ◽  
Potts Model ◽  
Triangular Lattice ◽  
Lattice Models ◽  
Range Order ◽  
Square Lattice ◽  
Long Range Order ◽  
Monte Carlo Studies ◽  
Antiferromagnetic Potts Model

AF Potts model MC dynamics at T=0 is considered. It is shown that q=3 square lattice and q=4 triangular lattice models are frozen for local MC algorithm. The nature of the previously discussed long-range order phases is examined and entropically favored states are considered.

scholarly journals Absence of classical long-range order in anS=12Heisenberg antiferromagnet on a triangular lattice

2014 ◽  
Vol 90 (18) ◽  
Author(s):  
Nobuo Suzuki ◽  
Fumitaka Matsubara ◽  
Sumiyoshi Fujiki ◽  
Takayuki Shirakura
Keyword(s):  
Long Range ◽  
Triangular Lattice ◽  
Range Order ◽  
Long Range Order

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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