Universal persistence exponents in an extremally driven system

Details Universal persistence exponents in an extremally driven system Universal persistence exponents in an extremally driven system

2001-11-12

arxiv.org/abs/cond-mat/0111213v1

Phys. Rev. E 65, 027104 (2002)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 6 figures. To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.65.027104

The local persistence R(t), defined as the proportion of the system still in its initial state at time t, is measured for the Bak--Sneppen model. For 1 and 2 dimensions, it is found that the decay of R(t) depends on one of two classes of initial configuration. For a subcritical initial state, R(t)\sim t^{-\theta}, where the persistence exponent \theta can be expressed in terms of a known universal exponent. Hence \theta is universal. Conversely, starting from a supercritical state, R(t) decays by the anomalous form 1-R(t)\sim t^{\tau_{\rm ALL}} until a finite time t_{0}, where \tau_{\rm ALL} is also a known exponent. Finally, for the high dimensional model R(t) decays exponentially with a non--universal decay constant.

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