Critical behaviour of the local magnetic susceptibility in a ferromagnetic film

The nearest-neighbour Ising model of a ferromagnetic film in which couplings between surface spins may differ from couplings between remaining spins is considered. Using the mean-field approximation, the local magnetic susceptibility defined as the derivative of the local magnetization with respect to the external uniform magnetic field is obtained. The behaviour of the local magnetic susceptibility near the ordinary, surface-bulk and surface phase transitions and in a range of temperatures where physical quantities have pseudocritical behaviour is discussed. The critical behaviour of the local magnetic susceptibility in a three-dimensional semi-infinite model is also given for comparison.