In the statistical physics of disordered systems, the random energy model is a toy model of a system with quenched disorder, such as a spin glass, having a first-order phase transition. It concerns the statistics of a collection of N spins (i.e. degrees of freedom σ σ ≡ ≡ { σ σ i } i = 1 N that can take one of two possible values σ σ i = ± ± 1 ) so that the number of possible states for the system is 2 N . The energies of such states are independent and identically distributed Gaussian random variables E x ∼ ∼ N ( 0 , N / 2 ) with zero mean and a variance of N / 2 . Many properties of this model can be computed exactly. Its simplicity makes this model suitable for pedagogical introduction of concepts like quenched disorder and replica symmetry.