Free energy, entropy, and magnetization of a one-dimensional Ising model of a diluted magnet

We consider a one-dimensional Ising model (chain) with the the nearest-neighbor interaction and with a random nonmagnetic dilution. We find the exact free energy of such a chain as a function of the impurity concentration, temperature, and the external magnetic field. In the case of antiferromagnetic interaction in the chain, we find the specific magnetization, the mean value of the product of neighboring spins, and the entropy as functions of these parameters. We study the residual system entropy.