“…Since m 1 and φ 1 are small, we may neglect higher orders terms proportional to them and their derivatives in the equations of motion 9 . In this case we would be neglecting the spin wave interactions.…”
Section: The Solutions and Their Stabilitymentioning
We study a recent generalization proposed for the XY model in two and three dimensions. Using both, the continuum limit and discrete lattice, we obtained the vortex configuration and shown that out-of-plane vortex solutions are deeply jeopardized whenever the parameter of generalization, L, is increased. The critical temperature for such models is calculated using the self consistent harmonic approximation. In both, two-and three-dimensional cases, such a temperature decreases with raising L. Our results are also compared with other approximated methods available in the literature.
“…Since m 1 and φ 1 are small, we may neglect higher orders terms proportional to them and their derivatives in the equations of motion 9 . In this case we would be neglecting the spin wave interactions.…”
Section: The Solutions and Their Stabilitymentioning
We study a recent generalization proposed for the XY model in two and three dimensions. Using both, the continuum limit and discrete lattice, we obtained the vortex configuration and shown that out-of-plane vortex solutions are deeply jeopardized whenever the parameter of generalization, L, is increased. The critical temperature for such models is calculated using the self consistent harmonic approximation. In both, two-and three-dimensional cases, such a temperature decreases with raising L. Our results are also compared with other approximated methods available in the literature.
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