On the existence of thermodynamics for the random energy model (Q1070679)
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scientific article; zbMATH DE number 3938213
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of thermodynamics for the random energy model |
scientific article; zbMATH DE number 3938213 |
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On the existence of thermodynamics for the random energy model (English)
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1984
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For \textit{B. Derrida}'s random energy model [Phys. Rev. Lett. 45, 79-82 (1980)], the authors prove that the finite size free energy \(n^{-1}\log \sum^{2^ n}_{i=1}\exp \{\beta n^{1/2}X_ i\}\), where \(X_ i\) are independent Gaussian variables, converges geometrically and in \(L^ p\), \(p\geq 1\), for all \(\beta >0\). This disproves a conjecture of myself, stated in ibid. 90, 125-159 (1983; Zbl 0526.60093).
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random energy model
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