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Письма в Журнал экспериментальной и теоретической физики, 2007, том 85, выпуск 5, страницы 314–319
(Mi jetpl990)
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Эта публикация цитируется в 12 научных статьях (всего в 12 статьях)
МЕТОДЫ ТЕОРЕТИЧЕСКОЙ ФИЗИКИ
The density of stationary points in a high-dimensional random energy landscape and the onset of glassy behaviour
Ya. V. Fyodorovab, H.-J. Sommersc, I. Williamsa a School of Mathematical Sciences, University of Nottingham, NG72RD Nottingham, England
b Petersburg Nuclear Physics Institute RAS
c University of Duisburg-Essen, Department of Physics
Аннотация:
We calculate the density of stationary points and minima of a $N\gg1$ dimensional Gaussian energy landscape. We use it to show that the point of zero-temperature replica symmetry breaking in the equilibrium statistical mechanics of a particle placed in such a landscape in a spherical box of size $L=R\sqrt N$ corresponds to the onset of exponential in $N$ growth of the cumulative number of stationary points, but not necessarily the minima. For finite temperatures we construct a simple variational upper bound on the true free energy of the $R=\infty$ version of the problem and show that this approximation is able to recover the position of the whole de-Almeida-Thouless line.
Поступила в редакцию: 29.01.2007
Образец цитирования:
Ya. V. Fyodorov, H.-J. Sommers, I. Williams, “The density of stationary points in a high-dimensional random energy landscape and the onset of glassy behaviour”, Письма в ЖЭТФ, 85:5 (2007), 314–319; JETP Letters, 85:5 (2007), 261–266
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jetpl990 https://www.mathnet.ru/rus/jetpl/v85/i5/p314
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