On the Efficiency of Topological Defect Formation in the Systems of   Various Size and (Quasi-) Dimensionality
  The experiments on verification of the Kibble-Zurek mechanism showed that topological defects are formed most efficiently in the systems of small size or low (quasi-)dimensionality, whereas in the macroscopic two- and three-dimensional samples a concentration of the defects, as a rule, is strongly suppressed. A reason for universality of such behavior can be revealed by considering a strongly-nonequilibrium symmetry-breaking phase transition in the simplest phi-4 field model. It is shown that the resulting distribution of the defects (domain walls) is formally reduced to the well-known Ising model, whose behavior changes dramatically in passing from a finite to infinite size of the system and from the low (D=1) to higher (D>=2) dimensionality. 
Yu.V. Dumin (Max-Planck-Institut, Dresden, Germany & University of   California, Los Angeles, USA), L.M. Svirskaya (Chelyabi...