Magnetic properties and the function q(x) of the generalised random-energy model

Abstract

The authors give a general expression for the free energy of the generalised random-energy model (GREM) in terms of the average partition function (Z) and the average squared partition function (Z2). Then, using the notion of the partial partition function, they show how one can introduced a magnetic field in the GREM. The de Almeida-Thouless line and the magnetisation in the spin glass phase are computer. The moments (Zp) of the partition function are calculated and they show that a replica calculation with a full breaking of replica symmetry leads to the correct free energy. The function q(x) is then computed.