Random energy model

In statistical physics of disordered systems is a toy model of a system with quenched disorder. It concerns the statistics of a system of $N$ particles, such that the number of possible states for the systems grow as $2^{N}$, while the Energy of sush states is a gaussian stochastic variable. The model has exact solution. Its simpicity makes this model suitable for pedagogical introduction of concepts like quenched disorder and replica symmetry.