We are interested in the transition with one single spinflip to a new state $j$ with energy $E_j$ $$\begin{equation*} \begin{array}{cccccccccc} \uparrow&\uparrow&\uparrow&\dots&\uparrow&\uparrow&\uparrow&\dots&\uparrow&\downarrow\\ 1&2&3&\dots& k-1&k&k+1&\dots&N-1&N\end{array} \end{equation*}$$ This change from one microstate $i$ (or spin configuration) to another microstate $j$ is the configuration space analogue to a random walk on a lattice. Instead of jumping from one place to another in space, we 'jump' from one microstate to another.