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

Scaling dynamics of domain walls in the cubic anistropy model