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 \Delta E=8J . \begin{equation*} E=-4J\hspace{1cm}\begin{array}{ccc} & \uparrow & \\ \uparrow & \uparrow & \uparrow\\ & \uparrow & \end{array} \hspace{1cm}\Longrightarrow\hspace{1cm} E=4J\hspace{1cm}\begin{array}{ccc} & \uparrow & \\ \uparrow & \downarrow & \uparrow\\ & \uparrow & \end{array} \end{equation*} The four other possibilities are as follows \begin{equation*} E=-2J\hspace{1cm}\begin{array}{ccc} & \uparrow & \\ \downarrow & \uparrow & \uparrow\\ & \uparrow & \end{array} \hspace{1cm}\Longrightarrow\hspace{1cm} E=2J\hspace{1cm}\begin{array}{ccc} & \uparrow & \\ \downarrow & \downarrow & \uparrow\\ & \uparrow & \end{array} \end{equation*} with \Delta E=4J , \begin{equation*} E=0\hspace{1cm}\begin{array}{ccc} & \uparrow & \\ \downarrow & \uparrow & \uparrow\\ & \downarrow & \end{array} \hspace{1cm}\Longrightarrow\hspace{1cm} E=0\hspace{1cm}\begin{array}{ccc} & \uparrow & \\ \downarrow & \downarrow & \uparrow\\ & \downarrow & \end{array} \end{equation*} with \Delta E=0 , \begin{equation*} E=2J\hspace{1cm}\begin{array}{ccc} & \downarrow & \\ \downarrow & \uparrow & \uparrow\\ & \downarrow & \end{array} \hspace{1cm}\Longrightarrow\hspace{1cm} E=-2J\hspace{1cm}\begin{array}{ccc} & \downarrow & \\ \downarrow & \downarrow & \uparrow\\ & \downarrow & \end{array} \end{equation*} with \Delta E=-4J and finally \begin{equation*} E=4J\hspace{1cm}\begin{array}{ccc} & \downarrow & \\ \downarrow & \uparrow & \downarrow\\ & \downarrow & \end{array} \hspace{1cm}\Longrightarrow\hspace{1cm} E=-4J\hspace{1cm}\begin{array}{ccc} & \downarrow & \\ \downarrow & \downarrow & \downarrow\\ & \downarrow & \end{array} \end{equation*} with \Delta E=-8J .