Scaling Dynamics of Domain Walls in the Cubic Anisotropy Model

TL;DR

This study explores the evolution of domain walls in the cubic anisotropy model, revealing that despite complex junctions, the walls tend to evolve self-similarly with a linear relation between characteristic length and time.

Contribution

It provides the first detailed computation of scaling exponents for domain walls in the cubic anisotropy model across multiple dimensions and compares them to simpler models.

Findings

Walls evolve toward a self-similar regime with L ~ t

Lattice structures with junctions do not alter the linear scaling law

Scaling exponents vary with N in the range 2 to 7

Abstract

We have investigated the dynamics of domain walls in the cubic anisotropy model. In this model a global O(N) symmetry is broken to a set of discrete vacua either on the faces, or vertices of a (hyper)cube. We compute the scaling exponents for $2\le N\le 7$ in two dimensions on grids of $2048^2$ points and compare them to the fiducial model of $Z_2$ symmetry breaking. Since the model allows for wall junctions lattice structures are locally stable and modifications to the standard scaling law are possible. However, we find that since there is no scale which sets the distance between walls, the walls appear to evolve toward a self-similar regime with $L\sim t$.