Simulating the symmetron: Domain walls and symmetry-restoring impurities

In this paper we study the dynamics of relativistic domain walls in the presence of static symmetry-restoring impurities. The field theory is precisely the same as what is known to cosmologists as the "symmetron model," whereby the usual Z sub(2) symmetry breaking potential is appended with a space-varying mass term (the space variation is set by the profile of the impurity, which we take to be a "tanh" function). After presenting the outcomes of a suite of different numerical experiments we have three main results: (1) domain walls pin to impurities, (2) domain wall necklaces can be energetically preferred configurations, and (3) impurities significantly modify the usual N sub(dw) [is proportional to] t super(-1) scaling law for random networks of domain walls.