Fractality in Persistence Decay and Domain Growth during Ferromagnetic Ordering: Dependence upon initial correlation

TL;DR

This study investigates how initial correlations influence persistence decay, domain growth, and fractal properties in ferromagnetic ordering of Ising models through Monte Carlo simulations in two and three dimensions.

Contribution

It reveals the dependence of fractal dimensionality and persistence decay exponents on initial correlation length and resolves a controversy in domain growth exponent in three dimensions.

Findings

Fractal dimensionality depends on initial correlation length.

Persistence decay exponent varies with initial conditions.

Resolved controversy on domain growth exponent in 3D.

Abstract

Dynamics of ordering in Ising model, following quench to zero temperature, have been studied via Glauber spin-flip Monte Carlo simulations in space dimensions $d=2$ and $3$. One of the primary objectives has been to understand phenomena associated with the persistent spins, viz., time decay in the number of unaffected spins, growth of the corresponding pattern and its fractal dimensionality, for varying correlation length in the initial configurations, prepared at different temperatures, at and above the critical value. It is observed that the fractal dimensionality and the exponent describing the power-law decay of persistence probability are strongly dependent upon the relative values of nonequilibrium domain size and the initial equilibrium correlation length. Via appropriate scaling analyses, these quantities have been estimated for quenches from infinite and critical temperatures. The above mentioned dependence is observed to be less pronounced in higher dimension. In addition to these findings for the local persistence, we present results for the global persistence as well. Further, important observations on the standard domain growth problem are reported. For the latter, a controversy in $d=3$, related to the value of the exponent for the power-law growth of the average domain size with time, has been resolved.