Recently I calculated the Ising Hamiltonian of a Hopf link. First, I colored the Hopf link in a checker board pattern and drew the Seifert surface from it. Considering the shaded regions as vertices and crossings as edges I drew a graph from the surface. Then I considered the vertices as spins and edges as interactions to derive an equivalent Ising model. From it I calculated the Hamiltonian. Then I became curious about the Ising Hamiltonians of two systems, a) an unknot and b) a set of two unknots. I don't see how can I convert an unknot into an Ising system. Any idea, anyone?
2026-03-26 12:46:56.1774529216
Hamiltonian of one and two unknots
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