Random Energy Model & Glass Transition

Derrida's REM: 2^N configurations each with energy drawn from a Gaussian. The exact free energy shows a phase transition at T_g = 1/(2√ln2): above T_g, entropy is extensive; below, the system freezes into a finite number of states. The replica trick captures this via n→0 analytic continuation.

Parameters

N (system size): 20 Temperature T: 0.85 J (energy scale): 1.00

T_g = J/(2√ln2) = —
Current T/T_g: —
Phase: —

Free energy density:
F/N = —
Entropy S/N: —