scholarly journals Why the Schwinger Boson mean field theory fails to describe the spin dynamics of the triangular lattice antiferromagnetic Heisenberg model?

2021 ◽  
Author(s):  
Qiu Zhang ◽  
Tao Li
Keyword(s):  
Field Theory ◽  
Triangular Lattice ◽  
Heisenberg Model ◽  
Spin Dynamics ◽  
Mean Field Theory ◽  
Mean Field ◽  
Antiferromagnetic Heisenberg Model

EFFECTIVE MEAN-FIELD THEORY BASED ON CUMULANT EXPANSION IN TREATING CLASSICAL HEISENBERG MODEL ON STACKED TRIANGULAR LATTICE

2011 ◽  
Vol 25 (06) ◽  
pp. 833-841
Author(s):  
LIMIN YANG ◽  
SONGQING ZHAO ◽  
KUN ZHAO ◽  
YUNXIA FAN ◽  
P. LI ◽  
...  
Keyword(s):  
Field Theory ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Spin System ◽  
Triangular Lattice ◽  
Heisenberg Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Cumulant Expansion ◽  
The Third

An effective mean-field theory based on cumulant expansion was used to deal with antiferromagnetic Heisenberg model on planar triangular lattice. The corrections of expansion were performed to the third order. By using the equation of the mean field condition, curves of internal energy E specific heat C staggered helicity K (order parameter) and the variational ratio of staggered helicity X were obtained when the proper values of effective external field were achieved. The calculated results showed that there were two phases (which were ordered antiferromagnetic phase and the disordered phase) in the spin system. The first order critical point is -kTc/Js = 1.65, the second is -kTc/Js = 1.35 and the third is -kTc/Js = 1.29, obviously closer to that of Monte Carlo simulation order by order. And also, the analytic expansion curves derived from this method exhibited higher proximity order by order to the Monte Carlo simulation. Such results showed that this method was a useful tool to obtain thermodynamically observables of spin system.

Pinwheel and herringbone structures of planar rotors with anisotropic interactions on a triangular lattice with vacancies

1984 ◽  
Vol 62 (9) ◽  
pp. 915-934 ◽  
Author(s):  
A. B. Harris ◽  
O. G. Mouritsen ◽  
A. J. Berlinsky
Keyword(s):  
Field Theory ◽  
Phase Diagram ◽  
Spin Wave ◽  
Triangular Lattice ◽  
Mean Field Theory ◽  
Mean Field ◽  
Wave Theory ◽  
Finite Domain ◽  
Unexpected Result ◽  
Spin Wave Theory

A variety of theoretical techniques, including Monte Carlo (MC), mean field theory, and spin-wave theory, are used to analyze the phase diagram of a system of planar rotors on a triangular lattice with vacancies. A simple anisotropic interaction, which mimics the electric quadrupole–quadrupole interaction for diatomic molecules confined to rotate in the plane of the surface, induces a herringbone-ordered structure for the pure (x = 1) system, whereas for x ≈ 0.75, if the vacancies are free to move, a 2 × 2 pinwheel structure is favored. For x = 0.75, MC calculations give a continuous transition with Ising exponents in agreement with renormalization group predictions for this universality class, the Heisenberg model with corner-type cubic anisotropy. Mean field theory gives the unexpected result that the pinwheel phase is stable only along the herringbone-disordered state coexistence line in the temperature versus chemical potential phase diagram. Spin-wave theory is used to show that there is, in fact, a finite domain of stability for the pinwheel phase, and a complete phase diagram, which encompasses all available information, is conjectured.

Spontaneous magnetization of ferromagnet in mean-field Heisenberg model

2019 ◽  
Vol 33 (04) ◽  
pp. 1950036 ◽  
Author(s):  
Artur P. Durajski ◽  
Anna B. Olesik ◽  
Anita E. Auguscik
Keyword(s):  
Field Theory ◽  
Magnetic Susceptibility ◽  
Curie Temperature ◽  
Heisenberg Model ◽  
Spontaneous Magnetization ◽  
Mean Field Theory ◽  
Mean Field ◽  
Function Technique ◽  
Heisenberg Ferromagnet ◽  
Temperature Dependences

The Heisenberg ferromagnet model has been studied theoretically using the Weiss mean-field theory and Green’s function technique. The equations for the Curie temperature, magnetization, and magnetic susceptibility were analytically derived. Moreover, we proved, that our results are useful in description of real materials. The calculated value of Curie temperature for [Formula: see text] alloy correspond well with the experimental results obtained recently on the base of the temperature dependences of magnetization.

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