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*}