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One old problem

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http://www.physicsforums.com/showthread.php?t=27021

I saw this problem and I think that is interesting but that have wrong formulation. But I'm not sure so I want to ask you. In renorm group method excange integral must be replaced by some other exchange integral and the number of spins become smaller. But I think that for this method lattice must be infinite. Am I right? I also don't know what term

[tex]\sum_{sg}\sigma_i\sigma_j\sigma_k\sigma_l[/tex] means.

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