Phase ordering percolation and an infinite domain wall in segregating
  binary Bose-Einstein condensates
  Percolation theory is applied to the phase-transition dynamics of domain
pattern formation in segregating binary Bose--Einstein condensates in
quasi-two-dimensional systems. Our finite-size-scaling analysis shows that the
percolation threshold of the initial domain pattern emerging from the dynamic
instability is close to 0.5 for strongly repulsive condensates. The percolation
probability is universally described with a scaling function when the
probability is rescaled by the characteristic domain size in the dynamic
scaling regime of the phase-ordering kinetics, independent of the
intercomponent interaction. It is revealed that an infinite domain wall
sandwiched between percolating domains in the two condensates has an noninteger
fractal dimension and keeps the scaling behavior during the dynamic scaling
regime. This result seems to be in contrast to the argument that the dynamic
scale invariance is violated in the presence of an infinite topological defect
in numerical cosmology.
