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Abstract: We investigate the persistence properties of critical d-dimensional systemsrelaxing from an initial state with non-vanishing order parameter e.g., themagnetization in the Ising model, focusing on the dynamics of the global orderparameter of a d-dimensional manifold. The persistence probability Pt showsthree distinct long-time decays depending on the value of the parameter \zeta =D-2+\eta-z which also controls the relaxation of the persistence probabilityin the case of a disordered initial state vanishing order parameter as afunction of the codimension D = d-d- and of the critical exponents z and \eta.We find that the asymptotic behavior of Pt is exponential for \zeta > 1,stretched exponential for 0 <= \zeta <= 1, and algebraic for \zeta < 0. Whereasthe exponential and stretched exponential relaxations are not affected by theinitial value of the order parameter, we predict and observe a crossoverbetween two different power-law decays when the algebraic relaxation occurs, asin the case d-=d of the global order parameter. We confirm via Monte Carlosimulations our analytical predictions by studying the magnetization of a lineand of a plane of the two- and three-dimensional Ising model, respectively,with Glauber dynamics. The measured exponents of the ultimate algebraic decaysare in a rather good agreement with our analytical predictions for the Isinguniversality class. In spite of this agreement, the expected scaling behaviorof the persistence probability as a function of time and of the initial valueof the order parameter remains problematic. In this context, thenon-equilibrium dynamics of the On model in the limit n->\infty and itssubtle connection with the spherical model is also discussed in detail.



Autor: Andrea Gambassi, Raja Paul, Gregory Schehr

Fuente: https://arxiv.org/







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