Article

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

Journal of Statistical Mechanics Theory and Experiment (Impact Factor: 1.87). 12/2010; DOI: 10.1088/1742-5468/2011/02/P02018

Source: arXiv

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**ABSTRACT:**The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles meet. The exact two-time correlation and response function in the one-dimensional coagulation-diffusion process are derived from the empty-interval-particle method. The main quantity is the conditional probability of finding an empty interval of n consecutive sites, if at distance d a site is occupied by a particle. Closed equations of motion are derived such that the probabilities needed for the calculation of correlators and responses, respectively, are distinguished by different initial and boundary conditions. In this way, the dynamical scaling of these two-time observables is analysed in the longtime ageing regime. A new generalised fluctuation-dissipation ratio with an universal and finite limit is proposed.Journal of Statistical Mechanics Theory and Experiment 12/2010; · 1.87 Impact Factor - [Show abstract] [Hide abstract]

**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. · 1.68 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schr\"odinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena.Nuclear Physics B 09/2010; · 4.33 Impact Factor

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