Casimir Force, Magnetization, and Susceptibility for \\ Ising Chain with an Impurity Atom in the Presence of an External Field

Abstract

The article contains exact results for the behavior of the Casimir force of Ising chain of $N$ atoms containing an impurity atom. The force is considered as a function of $N$ and on both the temperature $T$ and the external magnetic field $h$. The interactions between nearest neighbors within the chain are supposed to be of a ferromagnetic short-ranged type $J>0$. The impurity atom interacts with constants $J_{ia}$ with its nearest neighbors, where $J_{ia}$ can be both of ferromagnetic type, i.e., $J_{ia}>0$, as well as of antiferromagnetic type, i.e., $J_{ia}<0$. It turns out that the Casimir force can be both attractive or repulsive, depending on the sign and the magnitude of the ratio $J_{ia}/J$.