Non Markovian persistence in the diluted Ising model at criticality

Details Non Markovian persistence in the diluted Ising model at criticality Non Markovian persistence in the diluted Ising model at criticality

2005-07-19

arxiv.org/abs/cond-mat/0507445v2

Europhys. Lett., 72(5), 719 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 4 figures

Scientific paper

We investigate global persistence properties for the non-equilibrium critical dynamics of the randomly diluted Ising model. The disorder averaged persistence probability $\bar{{P}_c}(t)$ of the global magnetization is found to decay algebraically with an exponent $\theta_c$ that we compute analytically in a dimensional expansion in $d=4-\epsilon$. Corrections to Markov process are found to occur already at one loop order and $\theta_c$ is thus a novel exponent characterizing this disordered critical point. Our result is thoroughly compared with Monte Carlo simulations in $d=3$, which also include a measurement of the initial slip exponent. Taking carefully into account corrections to scaling, $\theta_c$ is found to be a universal exponent, independent of the dilution factor $p$ along the critical line at $T_c(p)$, and in good agreement with our one loop calculation.

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