Configurations
To better understand what is meant with a configuration,
consider first the case of the one-dimensional Ising model
with \( {\cal B}=0 \).
In general, a given configuration of \( N \) spins in one
dimension may look like
$$
\begin{equation*}
\begin{array}{cccccccccc}
\uparrow&\uparrow&\uparrow&\dots&\uparrow&\downarrow&\uparrow&\dots&\uparrow&\downarrow\\
1&2&3&\dots& i-1&i&i+1&\dots&N-1&N\end{array}
\end{equation*}
$$
In order to illustrate these features
let us further specialize to
just two spins.
With two spins, since each spin takes two values only,
we have \( 2^2=4 \) possible arrangements of the two spins.
These four possibilities are
$$
\begin{equation*}
1= \uparrow\uparrow\hspace{1cm}
2= \uparrow\downarrow\hspace{1cm}
3= \downarrow\uparrow\hspace{1cm}
4=\downarrow\downarrow
\end{equation*}
$$