Systems of Interacting Particles

This chapter presents two examples of the application of Boltzmann statistics to systems with nontrivial interactions between particles. The first example is a nonideal gas, treated approximately using a series expansion that we can visualize in terms of simple diagrams. The second example is a model of a ferromagnet as a collection of two-state particles interacting with their nearest neighbors. It is easy to solve this model exactly in one dimension, and to gain a semi-quantitative understanding of why the system magnetizes below a critical temperature in two or three dimensions. The most powerful tool for studying this model, however, is numerical simulation on a computer using a random-sampling algorithm based on the Boltzmann distribution.