Understanding Spin Product of Graphs: Solutions to Questions

[LagrangeEuler]

I don't understand this very well.

http://books.google.rs/books?id=vrc...page&q=spin product of graphs nolting&f=false

Can you explain me relation (6.93)? Tnx.

Is $$S_iS_jS_jS_k=4$$?

 

[matematikuvol]

No. You have sum.
So
Spins may take values +1 or -1. Because of that
result of
$$S_iS_jS_jS_k$$
is either +1 or -1.
For example
$$\sum_{S_1=-1,1}\sum_{S_2=-1,1}S_iS_{i+1}=-1 \cdot (-1)+(-1)\cdot 1+1\cdot(-1)+1-1 \cdot (-1)+(-1)\cdot 1+1\cdot(-1)=0$$
I don't know what that means in the graph case. If someone knows it would me nice to write down.