Emergence of long-range force laws from classical particle exchange

The analogy of classical repulsive interactions emerging from the exchange of mediating particles is revisited with a quantitative approach. Simulations are presented for a particular toy model which are accessible to undergraduate students at any level in the physics curriculum. Analytic treatment of the various regimes shows rigorously how effective force laws can emerge from an underlying microscopic model and should be accessible to advanced undergraduate physics majors. The analysis presented uses the concept of emergence as motivation for students to gain experience building and testing simplified models for complex physical processes.