Two Neighbor Segments with Equal Filling

Rewriting the spin permutation with the help of the Dirac identity, one can obtain the following spin Hamiltonian  

When n is increased, the form of the exchange integrals J and J2 is changed 

The increase in s leads to more complicated spin Hamiltonians. Thus, in the case of s=2, n=3 and p = 0, this Hamiltonian is of the form 

Therefore, the ferromagnetic state energy of the rectangular lattice formed by weakly interacting segments with equal filling should be equal to zero in the second PT order in t2. 

---