ABSTRACT
This chapter considers systems featuring inter-particle interactions. Statistical mechanics can treat interacting systems, but no one said it would be easy. Van der Waals reasoned that the pressure would be lowered by attractive interactions between atoms. A phase transition associated with purely repulsive interactions is known as the Kirkwood-Alder transition. Thus, the partition function of a one-dimensional collection of particles having hard core potentials can be solved exactly for nearest-neighbor interactions only. Many other types of magnetic phenomena occur as a result of interactions between moments located on lattice sites of crystals. It's straightforward to generalize to a one-dimensional system with arbitrarily distant interactions. The chapter introduces the Ising model of interacting degrees of freedom on a lattice, and the transfer matrix method of solution. It discusses how scattering experiments probe the structure of systems of interacting particles, and the approximate Ornstein-Zernike theory of the static structure factor.
