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- W2052076819 abstract "Finding the mean of the total number ${N}_{mathrm{tot}}$ of stationary points for $N$-dimensional random energy landscapes is reduced to averaging the absolute value of the characteristic polynomial of the corresponding Hessian. For any finite $N$ we provide the exact solution to the problem for a class of landscapes corresponding to the ``toy model'' of manifolds in a random environment. For $Nensuremath{gg}1$ our asymptotic analysis reveals a phase transition at some critical value ${ensuremath{mu}}_{c}$ of a control parameter $ensuremath{mu}$ from a phase with a finite landscape complexity: ${N}_{mathrm{tot}}ensuremath{sim}{e}^{Nensuremath{Sigma}}$, $ensuremath{Sigma}(ensuremath{mu}<{ensuremath{mu}}_{c})>0$ to the phase with vanishing complexity: $ensuremath{Sigma}(ensuremath{mu}>{ensuremath{mu}}_{c})=0$. Finally, we discuss a method of dealing with the modulus of the spectral determinant applicable to a broad class of problems." @default.
- W2052076819 created "2016-06-24" @default.
- W2052076819 creator A5011588658 @default.
- W2052076819 date "2004-06-15" @default.
- W2052076819 modified "2023-10-02" @default.
- W2052076819 title "Complexity of Random Energy Landscapes, Glass Transition, and Absolute Value of the Spectral Determinant of Random Matrices" @default.
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- W2052076819 doi "https://doi.org/10.1103/physrevlett.92.240601" @default.
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