Computational Physics Lectures: Statistical physics and the Ising Model

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Energy with PBC

In this case the energy for $E_1$ is different, we obtain namely $\begin{equation*} E_1=E_{\uparrow\uparrow}=-2J. \end{equation*}$ The other cases do also differ and we have $\begin{equation*} E_2=E_{\uparrow\downarrow}=+2J, \end{equation*}$ $\begin{equation*} E_3=E_{\downarrow\uparrow}=+2J, \end{equation*}$ and $\begin{equation*} E_4=E_{\downarrow\downarrow}=-2J. \end{equation*}$