Replica Symmetry Breaking Condition Exposed by Random Matrix Calculation of Landscape Complexity

@article{Fyodorov2007ReplicaSB,
  title={Replica Symmetry Breaking Condition Exposed by Random Matrix Calculation of Landscape Complexity},
  author={Yan V. Fyodorov and Ian Williams},
  journal={Journal of Statistical Physics},
  year={2007},
  volume={129},
  pages={1081-1116}
}
Abstract We start with a rather detailed, general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(≫1)-dimensional Gaussian landscape and confined by a spherically symmetric potential suitably growing at infinity. Then we employ random matrix methods to calculate the density of stationary points, as well as minima, of the associated energy surface. This is used to show that for a generic smooth, concave confining… 

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