Article

# Aging and stationary properties of non-equilibrium symmetrical three-state models

Journal of Statistical Mechanics Theory and Experiment (Impact Factor: 2.4). 12/2010; 2011(2). DOI: 10.1088/1742-5468/2011/02/P02018

Source: arXiv

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**ABSTRACT:**In this work we investigate critical aging properties of the two-dimensional spherical model with the long-range interaction, which decays at large distances rr by a power-law as r−3r−3. The model with an arbitrary initial order m0m0 is quenched from a very high temperature to the critical temperature TcTc. In the short-time regime, the magnetization increases with a logarithmic power law. The logarithmic corrections, which are dependent of m0m0, enter into the scaling behavior of two-time response and correlation functions. The long-time limit of the fluctuation–dissipation ratio is calculated. Three distinct types of aging are found at both criticality and low temperatures. Some universal scaling relations are tested. The crossover from the disordered initial state to the ordered state is discussed. Our two-dimensional results can be extended to the general dd-dimensional cases for the long-range interaction r−d−σr−d−σ with d=2σd=2σ. It is shown that the inclusion of this kind of long range interaction tends to the mean field behavior.Physica A: Statistical Mechanics and its Applications 10/2012; 391(20):4661–4674. DOI:10.1016/j.physa.2012.05.012 · 1.73 Impact Factor