Temporal correlations and persistence in the kinetic Ising model: the role of temperature

J. M. Drouffe; C. Godrèche

doi:10.1007/s100510170277

EPJ

Temporal correlations and persistence in the kinetic Ising model: the role of temperature

J. M. Drouffe¹ and C. Godrèche²^a

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

Received: 4 December 2000
Published online: 15 March 2001

Abstract

We study the statistical properties of the sum $S_t=\int_{0}^{t}{\rm d}t' \sigma_{t'}$ , that is the difference of time spent positive or negative by the spin $\sigma_{t}$ , 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 S_t and the first-passage statistics (persistence) of this quantity. We discuss successively the three regimes of high temperature ( $T> T_{\rm c}$ ), criticality ( $T=T_{\rm c}$ ), and low temperature ( $T< T_{\rm c}$ ). We discuss in particular the question of the temperature dependence of the persistence exponent θ, as well as that of the spectrum of exponents $\theta(x)$ , 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 $t^{-\theta-\frac12}$ . 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

Student Conference in Optics and Photonics 2024
October 2-4, 2024
Barcelona, Spain

EPJ

Temporal correlations and persistence in the kinetic Ising model: the role of temperature

Conference announcements