Spin product of graphs

LagrangeEuler

I don't understand this very well.

http://books.google.rs/books?id=vrcH...olting&f=false

Can you explain me relation (6.93)? Tnx.

Is [tex]S_iS_jS_jS_k=4[/tex]?

matematikuvol

No. You have sum.
So
Spins may take values +1 or -1. Because of that
result of
[tex]S_iS_jS_jS_k[/tex]
is either +1 or -1.
For example
[tex]\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[/tex]
I don't know what that means in the graph case. If someone knows it would me nice to write down.

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LagrangeEuler	Spin product of graphs I don't understand this very well. http://books.google.rs/books?id=vrcH...olting&f=false Can you explain me relation (6.93)? Tnx. Is [tex]S_iS_jS_jS_k=4[/tex]?

matematikuvol	No. You have sum. So Spins may take values +1 or -1. Because of that result of [tex]S_iS_jS_jS_k[/tex] is either +1 or -1. For example [tex]\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[/tex] I don't know what that means in the graph case. If someone knows it would me nice to write down.