Temporal correlations and persistence in the kinetic Ising model: the role of temperature |
| |
Authors: | JM Drouffe C Godrèche |
| |
Institution: | (1) Service de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France, FR;(2) Service de Physique de l'état Condensé, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France, FR |
| |
Abstract: | We study the statistical properties of the sum S
t =
dt'σ
t', that is the difference of time spent positive or negative by the spin σ
t, 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
( T > T
c), criticality ( T = T
c), and low temperature ( T < T
c). We discuss in particular the question of the temperature dependence of the persistence exponent , as well as that of the spectrum of exponents (x), in the low temperature phase. The probability that the temporal mean S
t/t was always larger than the equilibrium magnetization is found to decay as t
-
- ?. This yields a numerical determination of the persistence exponent 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.
Received 4 December 2000 |
| |
Keywords: | 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 |
本文献已被 SpringerLink 等数据库收录! |
|