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ABSTRACT: It is argued that systems whose elements are renewed according to an extremal criterion can generally be expected to exhibit longterm memory. This is verified for the minimal extremally driven model, which is first defined and then solved for all system sizes N>=2 and times t>=0, yielding exact expressions for the persistence R(t) = [1 + t/(N1)]1 and the twotime correlation function C(tw + t,tw) = (11/N)(N + tw)/(N + tw + t1). The existence of longterm memory is inferred from the scaling of C(tw + t,tw)~f(t/tw), denoting aging. Finally, we suggest ways of investigating the robustness of this mechanism when competing processes are present.Journal of Physics A General Physics 10/2000; 33(42). DOI:10.1088/03054470/33/42/102  [Show abstract] [Hide abstract]
ABSTRACT: We introduce the stronglyinteracting trap model, a version of Bouchaud's trap model for glasses [Bouchaud JP 1992 {\em J. Phys. I France {\bf 2}} 1705]. At finite temperatures the model exhibits glassy relaxation over intermediate timeframes but reaches a steady state at finite times. In limit of zero temperature and with a suitably renormalised timescale the model maps onto the BakSneppen model, widely studied in the context of selforganised criticality [Bak P and Sneppen K 1993 {\em Phys. Rev. Lett. {\bf 71}} 4083]. Hence zero temperature is a critical point in all dimensions. These claims are supported by mean field analysis of the stationary solution and numerical simulations of a finitedimensional lattice model. Comment: 16 pages in IOP format; 6 figuresJournal of Physics A General Physics 08/1999; DOI:10.1088/03054470/33/3/303
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2000

The University of Edinburgh
 School of Physics and Astronomy
Edinburgh, Scotland, United Kingdom
