The probability distribution of the partition function of the random energy model
- 21 June 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (12) , 1975-1981
- https://doi.org/10.1088/0305-4470/22/12/003
Abstract
The authors give the expression for both integer and non-integer moments of the partition function Z of the random energy model. In the thermodynamic limit, they find that the probability distribution P(Z) can be decomposed into two parts. For log Z-(log Z) finite, the distribution is independent of N, the size of the system, whereas for log Z-(log Z) positive and of order N, the distribution is Gaussian. These two parts match in the region 1<<log Z-(log Z)<<N where the distribution is exponential.Keywords
This publication has 15 references indexed in Scilit:
- Fluctuations in Derrida's random energy and generalized random energy modelsJournal of Statistical Physics, 1989
- Magnetic properties and the function q(x) of the generalised random-energy modelJournal of Physics C: Solid State Physics, 1986
- Solution of the generalised random energy modelJournal of Physics C: Solid State Physics, 1986
- Spin glasses with p-spin interactionsNuclear Physics B, 1985
- Sample to sample fluctuations in the random energy modelJournal de Physique Lettres, 1985
- The simplest spin glassNuclear Physics B, 1984
- Replica symmetry breaking and the nature of the spin glass phaseJournal de Physique, 1984
- Parisi's mean-field solution for spin glasses as an analytic continuation in the replica numberJournal of Physics A: General Physics, 1983
- Random-energy model: An exactly solvable model of disordered systemsPhysical Review B, 1981
- Random-Energy Model: Limit of a Family of Disordered ModelsPhysical Review Letters, 1980