We can also choose so-called periodic boundary conditions. This means that the neighbour to the right of \( s_N \) is assumed to take the value of \( s_1 \). Similarly, the neighbour to the left of \( s_1 \) takes the value \( s_N \). In this case the energy for the one-dimensional lattice reads $$ \begin{equation*} E_i =-J\sum_{j=1}^{N}s_js_{j+1}, \end{equation*} $$ and we obtain the following expression for the two-spin case $$ \begin{equation*} E=-J(s_1s_2+s_2s_1). \end{equation*} $$