Anisotropic dynamical scaling in a spin model with competing interactions

TL;DR

This paper investigates the anisotropic domain growth in a 2D Ising model with competing interactions, revealing different growth exponents and correlation behaviors in parallel and transverse directions, and applying an anisotropic scaling theory.

Contribution

It introduces an anisotropic extension of the Ohta-Jasnow-Kawasaki theory to describe correlation functions in a striped phase with competing interactions.

Findings

Domain growth exponents are 1/2 and 1/3 for different dynamics.

Correlation functions differ along and across stripes due to interface energy differences.

Anisotropic scaling theory successfully fits the simulation data.

Abstract

Results are presented for the kinetics of domain growth of a two-dimensional Ising spin model with competing interactions quenched from a disordered to a striped phase. The domain growth exponent are $\beta=1/2$ and $\beta=1/3$ for single-spin-flip and spin-exchange dynamics, as found in previous simulations. However the correlation functions measured in the direction parallel and transversal to the stripes are different as suggested by the existence of different interface energies between the ground states of the model. In the case of single-spin-flip dynamics an anisotropic version of the Ohta-Jasnow-Kawasaki theory for the pair scaling function can be used to fit our data.