Universal aging properties at a disordered critical point

Abstract

We investigate, analytically near the dimension $d_{uc}=4$ and numerically in $d=3$, the non equilibrium relaxational dynamics of the randomly diluted Ising model at criticality. Using the Exact Renormalization Group Method to one loop, we compute the two times $t,t_w$ correlation function and Fluctuation Dissipation Ratio (FDR) for any Fourier mode of the order parameter, of finite wave vector $q$. In the large time separation limit, the FDR is found to reach a non trivial value $X^{\infty }$ independently of (small) $q$ and coincide with the FDR associated to the the {\it total} magnetization obtained previously. Explicit calculations in real space show that the FDR associated to the {\it local} magnetization converges, in the asymptotic limit, to this same value $X^{\infty }$. Through a Monte Carlo simulation, we compute the autocorrelation function in three dimensions, for different values of the dilution fraction $p$ at $T_c(p)$. Taking properly into account the corrections to scaling, we find, according to the Renormalization Group predictions, that the autocorrelation exponent ${\lambda }_c$ is independent on $p$. The analysis is complemented by a study of the non equilibrium critical dynamics following a quench from a completely ordered state.

8 pages, 5 figures

References in corpus (3)

• Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models
• Aging in the glass phase of a 2D random periodic elastic system
• Nonequilibrium critical relaxation in the presence of extended defects

Cited by in corpus (14)

• Short-time dynamics and critical behavior of three-dimensional site-diluted Ising model
• Critical aging of Ising ferromagnets relaxing from an ordered state
• Critical aging of a ferromagnetic system from a completely ordered state
• Relaxational dynamics in 3D randomly diluted Ising models
• Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance
• Local and cluster critical dynamics of the 3d random-site Ising model
• Nonequilibrium critical dynamics with domain wall and surface
• Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state
• Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model
• Off-equilibrium relaxational dynamics with improved Ising Hamiltonian
• Non Markovian persistence in the diluted Ising model at criticality
• Physical ageing from generalised time-translation-invariance
• Static and dynamic structure factors in three-dimensional randomly diluted Ising models
• Dynamical critical behavior on the Nishimori point of frustrated Ising models