Peculiarities of Non-Equilibrium Critical Behavior for 3D Diluted Ising Model with Evolution from Low-Temperature Initial State

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The Monte Carlo description of aging properties in nonequilibrium critical behaviour of 3D site-diluted Ising model is considered with evolution from ordered initial state with wide range of spin concentrations. At first, it was shown, that pinning of domain walls on defects leeds to a sharp change of aging properties in diluted systems in comparison with pure system. Therefore, the asymptotic value of the fluctuation-dissipative relation becomes equal to null for diluted systems, while for pure system = 0.784(5).

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We investigate the nonequilibrium behaviour of the d-dimensional Ising model with purely dissipative dynamics during its critical relaxation from a magnetized initial configuration. The universal scaling forms of the two-time response and correlation functions of the magnetization are derived within the field-theoretical approach and the associated scaling functions are computed up to first order in the -expansion ( = 4 − d). Ageing behaviour is clearly displayed and the associated universal fluctuation–dissipation ratio tends to for long times. These results are confirmed by Monte Carlo simulations of the two-dimensional Ising model with Glauber dynamics, from which we find . The crossover to the case of relaxation from a disordered state is discussed and the crossover function for the fluctuation–dissipation ratio is computed within the Gaussian approximation.
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We discuss universal and non-universal critical exponents of a three dimensional Ising system in the presence of weak quenched disorder. Both experimental, computational, and theoretical results are reviewed. Special attention is paid to the results obtained by the field theoretical renormalization group approach. Different renormalization schemes are considered putting emphasis on analysis of divergent series obtained.
The values of a new universal parameter characterizing a nonequilibrium critical behavior, namely, the fluctuation-dissipation ratio specifying a fundamental relation between the dynamic response function and the correlation function, are calculated for the disordered three-dimensional Ising model. The analysis of the two-time dependence for autocorrelation functions and the ac susceptibility for the systems with spin densities p = 1.0, 0.8, and 0.6 shows the aging effects characterized by the anomalous slowing of relaxation in the system with the growth of the waiting time and the violation of the fluctuation-dissipation theorem. To improve the accuracy of the ac susceptibility calculations, the “thermal bath” technique has been used without introducing the applied magnetic field in the simulation. It has been shown that the structural defects lead to the pronounced enhancement of the aging effects.
Ageing phenomena and dynamical scaling behaviour are studied both in ferromagnets and in critical spin glasses. For the ferromagnetic systems we find that dynamical scaling functions measured after a quench into the ordered low temperature phase are in complete agreement with predictions coming from the recently proposed theory of local scale invariance. For a quench to the critical point corrections to these predictions are s hown to exist. Critical spin glasses are found to display the same ageing phenomenology as critical ferromagnets. Numerical evi- dence indicates that the concept of universality is weaker i n critical spin glasses than in critical ferromagnets.
Ageing properties of critical systems
  • P Calabrese
  • A Gambassi
P. Calabrese, A. Gambassi, Ageing properties of critical systems, J.Phys.A 38 (2005) R133-193.