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Summing up

The table lists the energy and magnetization for both free ends and periodic boundary conditions.

State Energy (FE) Energy (PBC) Magnetization
1= \uparrow\uparrow -J -2J 2
2=\uparrow\downarrow J 2J 0
$ 3=\downarrow\uparrow$ J 2J 0
$ 4=\downarrow\downarrow$ -J -2J -2