Knotted Configurations in the Continuous Heisenberg Spin Chain with Lower Bound of the Energy - Dandoloff, Rossen (European Journal of Applied Sciences, 2023)
When studying the classical Heisenberg spin models, we usually map the normalised unit vector, that represents the spin, on the tangent of a space curve. The total chirality of the curve (the spin configuration) i.e., the total momentum of the spin system, is a conserved quantity [1] and therefore self-crossing of the curve is not allowed. Using this fact and the non-contractibility of some closed loops in SO (3), we have proposed new topological spin configurations for the Heisenberg spin model [1]. Now we propose new topological spin configuration for the Heisenberg model, which represents a knot and has higher lower bound for the energy as the previously proposed configurations. The same analysis holds for a thin elastic rod that is bent to an open knot. PACS numbers: 75.10. Pq, 75.10. Hk, 02.40. Hw, 02.10. Kn