3,856 research outputs found
Persistence in q-state Potts model: A Mean-Field approach
We study the Persistence properties of the T=0 coarsening dynamics of one
dimensional -state Potts model using a modified mean-field approximation
(MMFA). In this approximation, the spatial correlations between the interfaces
separating spins with different Potts states is ignored, but the correct time
dependence of the mean density of persistent spins is imposed. For this
model, it is known that follows a power-law decay with time, where is the -dependent persistence exponent. We
study the spatial structure of the persistent region within the MMFA. We show
that the persistent site pair correlation function has the scaling
form for all values of the persistence
exponent . The scaling function has the limiting behaviour () and (). We then show within the
Independent Interval Approximation (IIA) that the distribution of
separation between two consecutive persistent spins at time has the
asymptotic scaling form where the
dynamical exponent has the form =max(). The behaviour of
the scaling function for large and small values of the arguments is found
analytically. We find that for small separations where =max(), while for large
separations , decays exponentially with . The
unusual dynamical scaling form and the behaviour of the scaling function is
supported by numerical simulations.Comment: 11 pages in RevTeX, 10 figures, submitted to Phys. Rev.
Persistence in One-dimensional Ising Models with Parallel Dynamics
We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic
nearest-neighbor Ising models with parallel dynamics. The probability P(t) that
a given spin has not flipped up to time t, when the system evolves from an
initial random configuration, decays as P(t) \sim 1/t^theta_p with theta_p
\simeq 0.75 numerically. A mapping to the dynamics of two decoupled A+A \to 0
models yields theta_p = 3/4 exactly. A finite size scaling analysis clarifies
the nature of dynamical scaling in the distribution of persistent sites
obtained under this dynamics.Comment: 5 pages Latex file, 3 postscript figures, to appear in Phys Rev.
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