Charge, junctions, and the scaling of domain wall networks

Abstract

It has been shown that superconducting domain walls in a model with U(1) x Z2 symmetry can form long-lived loops called kinky vortons from random initial conditions in the broken field and a uniform charged background in (2+1) dimensions. In this paper we investigate a similar model with a hyper-cubic symmetry coupled to an unbroken U(1) in which the domain walls can form junctions and hence a lattice. We call this model the charge-coupled cubic-anisotropy (CCCA) model. First, we present a detailed parametric study of the U(1) x Z2 model; features which we vary include the nature of the initial conditions and the coupling constants. This allows us to identify interesting parameters to vary in the more complicated, and hence more computationally intensive, CCCA models. In particular we find that the coefficient of the interaction term can be used to engineer three separate regimes: phase mixing, condensation and phase separation with the condensation regime corresponding to a single value of the coupling constant defined by the determinant of the quartic interaction terms being zero. We then identify the condensation regime in the CCCA model and show that, in this regime, the number of domain walls does not scale in the standard way if the initial conditions have a sufficiently high background charge. Instead of forming loops of domain wall, we find that, within the constraints of dynamic range, the network appears to be moving toward a glass-like configuration. We find that the results are independent of the dimension of the hyper-cube.