Universality of Domain Growth in Antiferromagnets with Spin-Exchange Kinetics

TL;DR

This study investigates the universal domain growth behavior in antiferromagnets with spin-exchange kinetics, revealing a consistent growth exponent of 1/2 across different mixture compositions and modeling approaches.

Contribution

It demonstrates the universality of domain growth in antiferromagnetic systems with Kawasaki kinetics and connects microscopic dynamics with coarse-grained free energy models.

Findings

Asymptotic growth exponent is 1/2 for domain size.

Scaling functions are independent of mixture composition.

Prolonged transients with different exponents can occur in asymmetric mixtures.

Abstract

We study phase ordering kinetics in symmetric and asymmetric binary mixtures, undergoing an order-disorder transition below the critical temperature. Microscopically, we model the kinetics via antiferromagnetic Ising model with Kawasaki spin-exchange kinetics. This conserves the composition while the order-parameter (staggered magnetization) is not conserved. The order-parameter correlation function and structure factor show dynamical scaling, and the scaling functions are independent of the mixture composition. The average domain size shows a power-law growth: $L_\sigma(t)\sim t^\alpha$. The asymptotic growth regime has $\alpha=1/2$, though there can be prolonged transients with $\alpha<1/2$ for asymmetric mixtures. Our unambiguous observation of the asymptotic universal regime is facilitated by using an accelerated Monte Carlo technique. We also obtain the coarse-grained free energy from the Hamiltonian, as a function of two order-parameters. The evolution of these order-parameters is modeled by using \textit{Model C} kinetics. Similar to the microscopic dynamics, the average domain size of the nonconserved order-parameter (staggered magnetization) field exhibits a power-law growth: $L_m(t)\sim t^{1/2}$ at later times, irrespective of the mean value of the conserved order-parameter (composition) field.