Random Energy Model

The Random Energy Model (abbreviated REM ) is a toy model in statistical physics of disordered systems, which was proposed by Bernard Derrida in 1980 .

It describes a system with the following three properties:

There are states with energies . ${\ displaystyle 2 ^ {N}}$ ${\ displaystyle E_ {i}}$

The energies are Gaussian . ${\ displaystyle E_ {i}}$

The energies are independent random variables.

The special thing about REM is that it can be solved exactly, and, despite its simplicity, important concepts of statistical physics as the frozen disorder ( quenched disorder ), replica symmetry and replica symmetry breaking can be studied (RSB) to him. If one looks at an SEM system in an external magnetic field, one finds a temperature-dependent phase transition between a frozen and a paramagnetic phase.

Individual evidence

↑ Derrida Random energy model: limit of a family of disordered models , Phys. Rev. Lett., Vol. 45 , 1980, pp. 79-82
↑ Derrida: Random energy model: an exactly solvable model of disordered systems , Phys. Rev. B 24 , 2613-2326 (1981)

literature

Anton Bovier Statistical Mechanics of disordered systems - a mathematical perspective , Cambridge University Press 2006

[1] Derrida Random energy model: limit of a family of disordered models , Phys. Rev. Lett., Vol. 45 , 1980, pp. 79-82

[2] Derrida: Random energy model: an exactly solvable model of disordered systems , Phys. Rev. B 24 , 2613-2326 (1981)