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

摘要

We study the statistical properties of the sum S_t = ∫_0~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 S_t 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 θ, as well as that of the spectrum of exponents θ(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~(-θ-1/2). 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.