The real paramagnet

In the process above, the lowest temperature attainable is obviously proportional to $\mu B_1/k_{\scriptscriptstyle B}$. In the ideal paramagnet, as $B$ is reduced the graph of $S$ against $T$ rises more and more steeply, going to a step function at $B=0$. But in any real paramagnet, there is a weak coupling between the spins which means that they prefer to be aligned with one another. If we remove the external field, this coupling acts like a weak internal field, and at low enough temperatures the spins will still be ordered. The strength of this coupling is then what governs the lowest attainable temperature.