Non Markovian persistence in the diluted Ising model at criticality

TL;DR

This paper studies the non-equilibrium critical dynamics of the diluted Ising model, revealing a new universal persistence exponent $ heta_c$ that characterizes disorder effects at criticality, supported by analytical and simulation results.

Contribution

It introduces the analytically computed persistence exponent $ heta_c$ for the disordered critical point, highlighting disorder-induced corrections to Markovian behavior.

Findings

$ar{P}_c(t)$ decays algebraically with exponent $ heta_c$

$ heta_c$ is universal and independent of dilution $p$

Monte Carlo simulations agree with analytical predictions

Abstract

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.