Non Markovian persistence in the diluted Ising model at criticality

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 $θ_c$ that we compute analytically in a dimensional expansion in $d=4-ε$. Corrections to Markov process are found to occur already at one loop order and $θ_c$ 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, $θ_c$ 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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