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Five possible energy differences

To see this, select first a random spin position x,y and assume that this spin and its nearest neighbors are all pointing up. The energy for this configuration is E=4J. Now we flip this spin as shown below. The energy of the new configuration is E=4J, yielding ΔE=8J. E=4JE=4J The four other possibilities are as follows E=2JE=2J with ΔE=4J, E=0E=0 with ΔE=0, E=2JE=2J with ΔE=4J and finally E=4JE=4J with ΔE=8J.