Random Energy Model

The Random Energy Model (REM), introduced by Derrida (1980), assigns a random Gaussian energy to each of the 2^N configurations of N Ising spins, independently: E_α ~ N(0, N·J²/2), α = 1,...,2^N This is the p→∞ limit of the p-spin model. The REM is exactly solvable: it has a phase transition at β_c = √(2 ln 2) / J. Below T_c, the partition function is dominated by O(1) frozen states (a glass phase). Above T_c, exponentially many states contribute. The minimum energy scales as E_min ~ -N·J·√(ln 2).