https://doi.org/10.1007/s100510170277
Temporal correlations and persistence in the kinetic Ising model: the role of temperature
1
Service de Physique Théorique,
CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
2
Service de Physique de l'État Condensé,
CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
Corresponding author: a godreche@spec.saclay.cea.fr
Received:
4
December
2000
Published online: 15 March 2001
We study the statistical properties of the sum
,
that is the difference of time spent positive or negative
by the spin 
,
located at a given site of a D-dimensional Ising model
evolving under Glauber dynamics from a random initial configuration.
We investigate the distribution of St and
the first-passage statistics (persistence) of this
quantity.
We discuss successively the three regimes of high temperature
(
), criticality (
), and low temperature (
).
We discuss in particular the question of the temperature dependence of the
persistence exponent θ, as well as that of the spectrum of exponents
, in the low temperature phase.
The probability that the temporal mean St/t was always larger
than the equilibrium magnetization is found to decay as 
.
This yields a numerical determination of the
persistence exponent θ in the whole low temperature phase,
in two dimensions, and above the roughening transition,
in the low-temperature phase of the three-dimensional Ising model.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 75.10.Hk – Classical spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
