Dynamic crossover in the global persistence at criticalityR. Paul1, A. Gambassi2, 3 and G. Schehr4
1 BIOMS, IWR, Ruprecht-Karls-Universität - 69120 Heidelberg, Germany
2 Max-Planck-Institut für Metallforschung - Heisenbergstr. 3, 70569 Stuttgart, Germany
3 Institut für Theoretische und Angewandte Physik, Universität Stuttgart - Pfaffenwaldring 57, 70569 Stuttgart, Germany
4 Laboratoire de Physique Théorique (UMR du CNRS 8627), Université de Paris-Sud - 91405 Orsay Cedex, France
received 22 January 2007; accepted in final form 12 February 2007; published April 2007
published online 13 March 2007
We investigate the global persistence properties of critical systems relaxing from an initial state with non-vanishing value of the order parameter (e.g., the magnetization in the Ising model). The persistence probability of the global order parameter displays two consecutive regimes in which it decays algebraically in time with two distinct universal exponents. The associated crossover is controlled by the initial value m0 of the order parameter and the typical time at which it occurs diverges as m0 vanishes. Monte Carlo simulations of the two-dimensional Ising model with Glauber dynamics display clearly this crossover. The measured exponent of the ultimate algebraic decay is in rather good agreement with our theoretical predictions for the Ising universality class.
05.70.Jk - Critical point phenomena.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).
© Europhysics Letters Association 2007