Theory of Adiabatic Susceptibility

A general proof of the equivalence between ${\chi }_S$ and ${\chi }_{\mathrm{iso}}$ is presented in the framework of statistical thermodynamics. It is based on the observation that transitions do occur during adiabatic processes due to the neglected small interactions which can hardly be included in the acutal Hamiltonian. A new expression is found for ${\chi }_{\mathrm{iso}}$ which is proved to coincide with ${\chi }_S$ and which is rederived straightforwardly from the ergodic theorem. As an example, a system of spins with a magnetic interaction under a strong magnetic field is considered by means of the perturbation method and shown to give consistent results.