Spontaneous formation of domain wall lattices in two spatial dimensions

Abstract

We show that the process of spontaneous symmetry breaking can trap a field theoretic system in a highly non-trivial state containing a lattice of domain walls. In one large compact space dimension, a lattice is inevitably formed. In two dimensions, the probability of lattice formation depends on the ratio of sizes L_x, L_y of the spatial dimensions. We find that a lattice can form even if R=L_y/L_x is of order unity. We numerically determine the number of walls in the lattice as a function of L_x and L_y.

arXiv comment6 pages, 6 figures. Background material added and minor corrections included. Final version to be published in Phys. Rev. D

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• Magnetic monopole - domain wall collisions
• Domain walls and fermion scattering in Grand Unified models
• The Creation of Defects with Core Condensation