• Journal of Magnetics
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• 제6권4호
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• pp.119-121
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• 2001

Monte Carlo simulation was employed to study the phase transition in the classical Heisenberg ferromagnet with variable interlayer interactions. The measured transition temperatures show a strong logarithmic dependence on J/J'where J and J'are the intralayer and the interlayer exchange interaction, respectively. The results were compared with the theoretical expectations and an empirical formula for the critical coupling was stained.

• 대한수학회보
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• 제61권2호
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• pp.541-556
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• 2024

In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain $-{\Delta}u+V(x)u-{\frac{u}{\sqrt{1-u^2}}}{\Delta}{\sqrt{1-u^2}}={\lambda}{\mid}u{\mid}^{p-2}u$, x ∈ ℝ^N, where 2 ≤ p < 2^*, N ≥ 3. By the Ekeland variational principle, the cut off technique, the change of variables and the L^∞ estimate, we study the existence of positive solutions. Here, we construct the L^∞ estimate of the solution in an entirely different way. Particularly, all the constants in the expression of this estimate are so well known.