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# Influence of disorder on ageing and memory effects in non-equilibrium critical dynamics of 3D Ising model relaxing from an ordered state

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## Abstract

We have performed a numerical investigation of the influence of disorder on the dynamical non-equilibrium evolution of a 3D site-diluted Ising model from a low-temperature initial state with magnetization m 0 = 1. It is shown that two-time dependences of the autocorrelation and integrated response functions for systems with spin concentrations p = 1.0, 0.95, 0.8, 0.6 and 0.5 demonstrate ageing properties with anomalous slowing-down relaxation and violation of the fluctuation-dissipation ratio. It was revealed that during non-equilibrium critical dynamics in the long-time regime the autocorrelation functions for diluted systems are extremely slow due to the pinning of domain walls on impurity sites. We have found that the fluctuation-dissipation ratio for diluted systems with spin concentration p < 1 while the pure system is characterized by . The autocorrelation function power-law delay becomes the same as for the time dependence of the magnetization in the critical point and is characterized by exponent . Also, for diluted systems we reveal memory effects for critical evolution in the ageing regime with realization of cyclic temperature change and quenching at .

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1 Laboratoire de Physique des Matériaux,* Université Henri Poincaré Nancy I, B.P. 239, F-54506 Vandœuvre lès Nancy Cedex, France*2 Isaac Newton Institute of Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, UK 3 Dipartamento di Fisica/INFN—Sezione di Firenze, Università di Firenze, I-50019 Sesto Fiorentino, Italy 4 INFM-SMC-CNR and Dipartamento di Fisica, Università di Roma 'La Sapienza', Piazzale A. Moro 2, I-00185 Roma, Italy 5 Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, Staudtstraße 7B3, D-91058 Erlangen, Germany 6 Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0435, USA
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Description of nonequilibrium critical behaviour in disordered systems by the theoretical methods
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