Non Markovian persistence in the diluted Ising model at criticality

Abstract

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 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.

7 pages, 4 figures

References in corpus (4)

• Ageing Properties of Critical Systems
• Universal aging properties at a disordered critical point
• Functional Renormalization for pinned elastic systems away from their steady states
• Aging in the glass phase of a 2D random periodic elastic system

Cited by in corpus (8)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Short-time dynamics and critical behavior of three-dimensional site-diluted Ising model
• Local Persistence in the Directed Percolation Universality Class
• Non-equilibrium critical dynamics in disordered ferromagnets
• Non-markovian global persistence in phase-ordering kinetics
• From Markovian to non-Markovian persistence exponents
• Dynamic crossover in the persistence probability of manifolds at criticality
• Dynamical critical behavior on the Nishimori point of frustrated Ising models