Formation of domain wall lattices

We study the formation of domain walls in a phase transition in which an ${S}_{5}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry is spontaneously broken to ${S}_{3}\ifmmode\times\else\texttimes\fi{}{S}_{2}.$ In one compact spatial dimension we observe the formation of a stable domain wall lattice. In two spatial dimensions we find that the walls form a network with junctions, there being six walls to every junction. The network of domain walls evolves so that junctions annihilate antijunctions. The final state of the evolution depends on the relative dimensions of the simulation domain. In particular we never observe the formation of a stable lattice of domain walls for the case of a square domain but we do observe a lattice if one dimension is somewhat smaller than the other. During the evolution, the total wall length in the network decays with time as ${t}^{\ensuremath{-}0.71},$ as opposed to the usual ${t}^{\ensuremath{-}1}$ scaling typical of regular ${Z}_{2}$ networks.