Spontaneous formation of domain wall lattices in two spatial dimensions

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

The Thermodynamics of Cosmic String densities in U(1) Scalar Field Theory

We present a full characterization of the phase transition in U(1) scalar field theory and of the associated vortex string thermodynamics in 3D. We show that phase transitions in the string densities exist and measure their critical exponents, both for the long string and the short loops. Evidence for a natural separation between these two string populations is presented. In particular our results strongly indicate that an infinite string population will only exist above the critical temperature. Canonical initial conditions for cosmic string evolution are show to correspond to the infinite temperature limit of the theory.Comment: 4 pages, 4 figures, RevTe

Kinky Brane Worlds

We present a toy model for five-dimensional heterotic M-theory where bulk three-branes, originating in 11 dimensions from M five-branes, are modelled as kink solutions of a bulk scalar field theory. It is shown that the vacua of this defect model correspond to a class of topologically distinct M-theory compactifications. Topology change can then be analysed by studying the time evolution of the defect model. In the context of a four-dimensional effective theory, we study in detail the simplest such process, that is the time evolution of a kink and its collision with a boundary. We find that the kink is generically absorbed by the boundary thereby changing the boundary charge. This opens up the possibility of exploring the relation between more complicated defect configurations and the topology of brane-world models.Comment: 31 pages, Latex, 6 eps-figure

The Creation of Defects with Core Condensation

Defects in superfluid 3He, high-Tc superconductors, QCD colour superfluids and cosmic vortons can possess (anti)ferromagnetic cores, and their generalisations. In each case there is a second order parameter whose value is zero in the bulk which does not vanish in the core. We examine the production of defects in the simplest 1+1 dimensional scalar theory in which a second order parameter can take non-zero values in a defect core. We study in detail the effects of core condensation on the defect production mechanism.Comment: 9 pages, 7 figures, small corrections, 2 references added, final version to be published in PR

Predicting the critical density of topological defects in O(N) scalar field theories

O(N) symmetric $\lambda \phi^4$ field theories describe many critical phenomena in the laboratory and in the early Universe. Given N and $D\leq 3$, the dimension of space, these models exhibit topological defect classical solutions that in some cases fully determine their critical behavior. For N=2, D=3 it has been observed that the defect density is seemingly a universal quantity at T_c. We prove this conjecture and show how to predict its value based on the universal critical exponents of the field theory. Analogously, for general N and D we predict the universal critical densities of domain walls and monopoles, for which no detailed thermodynamic study exists. This procedure can also be inverted, producing an algorithm for generating typical defect networks at criticality, in contrast to the canonical procedure, which applies only in the unphysical limit of infinite temperature.Comment: 4 pages, 3 figures, uses RevTex, typos in Eq.(11) and (14) correcte

Decoherence, tunneling and noise-activation in a double-potential well at high and zero temperature

We study the effects of the environment on tunneling in an open system described by a static double-well potential. We describe the evolution of a quantum state localized in one of the minima of the potential at $t=0$, both in the limits of high and zero environment temperature. We show that the evolution of the system can be summarized in terms of three main physical phenomena, namely decoherence, quantum tunneling and noise-induced activation, and we obtain analytical estimates for the corresponding time-scales. These analytical predictions are confirmed by large-scale numerical simulations, providing a detailed picture of the main stages of the evolution and of the relevant dynamical processes.Comment: Version to appear in Phys. Rev. E. 15 pages, 12 figures (low quality due to upload size limitations). Good quality figures in a pdf file can be downloaded from http://www.df.uba.ar/users/lombardo/tunne

On formation of domain wall lattices

We study the formation of domain walls in a phase transition in which an S_5\times Z_2 symmetry is spontaneously broken to S_3\times S_2. In one compact spatial dimension we observe the formation of a stable domain wall lattice. In two spatial dimensions we find that the walls form a network with junctions, there being six walls to every junction. The network of domain walls evolves so that junctions annihilate anti-junctions. The final state of the evolution depends on the relative dimensions of the simulation domain. In particular we never observe the formation of a stable lattice of domain walls for the case of a square domain but we do observe a lattice if one dimension is somewhat smaller than the other. During the evolution, the total wall length in the network decays with time as t^{-0.71}, as opposed to the usual t^{-1} scaling typical of regular Z_2 networks.Comment: 7 pages, 4 figures. Minor changes, final version accepted for publication in Phys. Rev.