Random Energy Model — Derrida's Glass Transition

2^N configurations with Gaussian energies; sharp transition at T_g = 1/√(2 ln 2)

T_glass: — F(T): — Configs: — Phase: —
About: Derrida's Random Energy Model (1980) assigns independent Gaussian energies E_α ~ N(0, N/2) to each of the 2^N spin configurations. Despite its simplicity, it has an exact solution showing a sharp glass transition at T_g = 1/√(2 ln 2) ≈ 0.849. Above T_g, all configurations contribute to the partition function (liquid phase). Below T_g, only the few lowest-energy configurations dominate — the system freezes into a glass. This is the simplest model capturing replica symmetry breaking.