Calculate the exact zero field partition function of the one-dimensional Ising model on a periodic chain of \(n\) spins using equation (13.2.5) and write \(Q_{N}(0, T)\) in the form of equation (13.4.52). Show that for \(x \rightarrow 1\), the partition function \(\rightarrow 2^{n}\). Evaluate the microcanonical entropy \(S(q) / k=\ln g_{q}\) and plot it for the case \(n=16\).