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The probability distribution of the partition function of the random energy model

E Gardner and B Derrida

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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.


PACS

02.50.Ng Distribution theory and Monte Carlo studies

05.70.Ce Thermodynamic functions and equations of state

02.50.Cw Probability theory

MSC

60Exx Distribution theory (See also 62Exx, 62Hxx)

82C35 Irreversible thermodynamics, including Onsager-Machlup theory

Subjects

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 12 (21 June 1989)



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