Role of initial correlation in coarsening of a ferromagnet

Abstract

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions d = 2 and 3, on square and simple cubic lattices. Results for the persistence probability and the domain growth are discussed for quenches to various temperatures (T-f) below the critical one (T-c), from different initial temperatures T-i >= T-c. In long time limit, for T-i > T-c, the persistence probability exhibits power-law decay with exponents theta similar or equal to 0.22 and similar or equal to 0.18 in d = 2 and 3, respectively. For finite T-i, the early time behavior is a different power-law whose life-time diverges and exponent decreases as T-i -> T-c. The two steps are connected via power-law as a function of domain length and the crossover to the second step occurs when this characteristic length exceeds the equilibrium correlation length at T = T-i. T-i = T-c is expected to provide a new universality class for which we obtain theta theta(c) similar or equal to 0.035 in d = 2 and similar or equal to 0.105 in d = 3. The time dependence of the average domain size l, however, is observed to be rather insensitive to the choice of T-i.