Edwards-Anderson Hamiltonian of a Hopf link

Hi,

I was calculating the Edwards-Anderson Hamiltonian of a Hopf link. A hopf link is like attachment 1. I have drawn the Seifert surface of that link. The surface is shown in attachment 2. It also contains the Boltzmann weight. So, this is an Ising model. I am confused as there are more than one interaction between a pair of sites. How will I keep that consideration when I calculate the Edwards-Anderson Hamiltonian.

Thanks in advance for your answers.

Attached Images

hopf_link.jpg (75.1 KB)

Attached Files

hopf-seifert-pattern-1-oriented-boltzman.pdf (16.0 KB)