Free energy and entropy for an impurity in a periodic background in one dimension
In this paper, we continue our study of periodic lattices formed by delta functions and their derivatives in (1+1) dimensions. Such systems are interesting as allowing for investigation of complicated problems in quite simple terms. Specifically, we consider the free energy of a single impurity in the background of such lattice. After developing the necessary technical tools, we consider as an example a specific case and found that the free energy shows a non monotone behavior as function of the temperature.