A Tomography of the GREM: Beyond the REM Conjecture
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In a companion paper we proved that in a large class of Gaussian disordered spin systems the local statistics of energy values near levels N1/2+α with α<1/2 are described by a simple Poisson process. In this paper we address the issue as to whether this is optimal, and what will happen if α=1/2. We do this by analysing completely the Gaussian Generalised Random Energy Models (GREM). We show that the REM behaviour persists up to the level βcN, where βc denotes the critical temperature. We show that, beyond this value, the simple Poisson process must be replaced by more and more complex mixed Poisson point processes.
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- 2.Borgs, C., Chayes, J.T., Mertens, S., Nair, C.: Proof of the local REM conjecture for number partitioning II: Growing energy scales. http://arxiv.org/list/cond-mat/0508600, 2005
- 6.Daley, D.J., Vere-Jones, D.: An introduction to the theory of point processes. Springer Series in Statistics, Berlin-Heidelberg New York: Springer-Verlag, 1988Google Scholar
- 7.Derrida, B.: Random-energy model: an exactly solvable model of disordered systems. Phys. Rev. B (3), 24(5), 2613–2626 (1981)Google Scholar
- 9.Leadbetter, M.R., Lindgren, G., Rootzén, H.: Extremes and related properties of random sequences and processes. Springer Series in Statistics. New York: Springer-Verlag, 1983Google Scholar
- 10.Kallenberg, O.: Random Measures. Fourth ed., Berlin: Akademie Verlag, 1986Google Scholar