Europhys. Lett.
Volume 72, Number 5, December 2005
Page(s) 719 - 725
Section General
Published online 28 October 2005
Europhys. Lett., 72 (5), pp. 719-725 (2005)
DOI: 10.1209/epl/i2005-10304-y

Non-Markovian persistence in the diluted Ising model at criticality

R. Paul and G. Schehr

Theoretische Physik, Universität des Saarlandes - 66041 Saarbrücken, Germany

received 20 July 2005; accepted in final form 3 October 2005
published online 28 October 2005

We investigate global persistence properties for the non-equilibrium critical dynamics of the randomly diluted Ising model. The disorder-averaged persistence probability $\overline{{P}_c}(t)$ 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 universal, independent of the dilution factor p along the critical line at Tc(p), and in good agreement with our one-loop calculation.

05.70.Jk - Critical point phenomena.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).
75.10.Nr - Spin-glass and other random models.

© EDP Sciences 2005