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 $\mathbb{Z}_2$ 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 modifies the usual
${N}_{\rm dw}\propto t^{-1}$ scaling law for random networks of domain walls.
