We can relate observables to various derivatives of the partition function and the free energy. When a given derivative of the free energy or the partition function is discontinuous or diverges (logarithmic divergence for the heat capacity from the Ising model) we talk of a phase transition of order of the derivative. A first-order phase transition is recognized in a discontinuity of the energy, or the first derivative of \( F \). The Ising model exhibits a second-order phase transition since the heat capacity diverges. The susceptibility is given by the second derivative of \( F \) with respect to external magnetic field. Both these quantities diverge.