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 $$ \begin{equation*} 1= \uparrow\uparrow\hspace{1cm} 2= \uparrow\downarrow\hspace{1cm} 3= \downarrow\uparrow\hspace{1cm} 4=\downarrow\downarrow \end{equation*} $$