Domain Wall Networks Research Articles

X-type andY-type junction stability in domain wall networks

We develop an analytic formalism that allows one to quantify the stability properties of X-type and Y-type junctions in domain wall networks in two dimensions. A similar approach might be applicable to more general defect systems involving junctions that appear in a range of physical situations, for example, in the context of F- and D-type strings in string theory. We apply this formalism to a particular field theory, Carter's pentavac model, where the strength of the symmetry breaking is governed by the parameter $|\epsilon|< 1$. We find that for low values of the symmetry breaking parameter X-type junctions will be stable, whereas for higher values an X-type junction will separate into two Y-type junctions. The critical angle separating the two regimes is given by \alpha_c = 293^{\circ}\sqrt{|\epsilon|}$ and this is confirmed using simple numerical experiments. We go on to simulate the pentavac model from random initial conditions and we find that the dominant junction is of \ytype for $|\epsilon| \geq 0.02$ and is of \xtype for $|\epsilon| \leq 0.02$. We also find that for small $\epsilon$ the evolution of the number of domain walls $\qsubrm{N}{dw}$ in Minkowski space does not follow the standard $\propto t^{-1}$ scaling law with the deviation from the standard lore being more pronounced as $\epsilon$ is decreased. The presence of dissipation appears to restore the $t^{-1}$ lore.

Scaling properties of domain wall networks

We revisit the cosmological evolution of domain wall networks, taking advantage of recent improvements in computing power. We carry out high-resolution field theory simulations in two, three and four spatial dimensions to study the effects of dimensionality and damping on the evolution of the network. Our results are consistent with the expected scale-invariant evolution of the network, which suggests that previous hints of deviations from this behavior may have been due to the limited dynamical range of those simulations. We also use the results of very large ($1024^3$) simulations in three cosmological epochs to provide a calibration for the velocity-dependent one-scale model for domain walls: we numerically determine the two free model parameters to have the values $c_w=0.5\pm0.2$ and $k_w=1.1\pm0.3$.

Evolution of string-wall networks and axionic domain wall problem

We study the cosmological evolution of domain walls bounded by strings which arise naturally in axion models. If we introduce a bias in the potential, walls become metastable and finally disappear. We perform two dimensional lattice simulations of domain wall networks and estimate the decay rate of domain walls. By using the numerical results, we give a constraint for the bias parameter and the Peccei-Quinn scale. We also discuss the possibility to probe axion models by direct detection of gravitational waves produced by domain walls.

ModulatedC60monolayers on Si(111)3×3-Au reconstructions

Adsorption of ${\mathrm{C}}_{60}$ onto the Si(111)-$\ensuremath{\alpha}$-$\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$-Au surface with a high density of domain walls and its In-induced modification, a domain-wall-free Si(111)$\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$-(Au,In) surface, has been studied using scanning tunneling microscopy (STM). Adsorbed ${\mathrm{C}}_{60}$ have been found to form close-packed hexagonal arrays displaying specific patterns of ${\mathrm{C}}_{60}$ having different dim-bright STM contrast. On the Si(111)-$\ensuremath{\alpha}$-$\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$-Au surface, the dim-bright ${\mathrm{C}}_{60}$ pattern replicates the domain-wall network of the substrate surface and has plausibly an electronic origin. On the homogeneous Si(111)$\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$-(Au,In) surface, a Moir\'e pattern of a two-dimensional lattice develops, which indicates periodic occupation of the same regular adsorption sites on the surface. Here, the dim-bright ${\mathrm{C}}_{60}$ contrast is associated plausibly with different topographic heights of the molecules. In the case of the multilayer ${\mathrm{C}}_{60}$ films, the dim-bright ${\mathrm{C}}_{60}$ patterns of the first ${\mathrm{C}}_{60}$ monolayer have been found to be inherited with gradual smearing in the next ${\mathrm{C}}_{60}$ layers.

Domain wall network evolution in (N+1)-dimensional FRW universes

We develop a velocity-dependent one-scale model for the evolution of domain wall networks in flat expanding or collapsing homogeneous and isotropic universes with an arbitrary number of spatial dimensions, finding the corresponding scaling laws in frictionless and friction dominated regimes. We also determine the allowed range of values of the curvature parameter and the expansion exponent for which a linear scaling solution is possible in the frictionless regime.

Charge, junctions, and the scaling of domain wall networks

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.

Impact of string and monopole-type junctions on domain wall dynamics: Implications for dark energy

We investigate the potential role of string and monopole-type junctions in the frustration of domain wall networks using a velocity-dependent one-scale model for the characteristic velocity, v, and the characteristic length, L, of the network. We show that, except for very special network configurations, v2≲(HL)2≲(ρσ+ρμ)/ρm where H is the Hubble parameter and ρσ, ρμ and ρm are the average density of domain walls, strings and monopole-type junctions. We further show that if domain walls are to provide a significant contribution to the dark energy without generating exceedingly large CMB temperature fluctuations then, at the present time, the network must have a characteristic length L0≲10Ωσ0−2/3 kpc and a characteristic velocity v0≲10−5Ωσ0−2/3 where Ωσ0=ρσ0/ρc0 and ρc is the critical density. In order to satisfy these constraints with Ωσ0∼1, ρm0 would have to be at least 10 orders of magnitude larger than ρσ0, which would be in complete disagreement with observations. This result provides very strong additional support for the conjecture that no natural frustration mechanism, which could lead to a significant contribution of domain walls to the dark energy budget, exists.

Evolution of domain wall networks: The Press-Ryden-Spergel algorithm

The Press-Ryden-Spergel (PRS) algorithm is a modification to the field theory equations of motion, parametrized by two parameters ($\ensuremath{\alpha}$ and $\ensuremath{\beta}$), implemented in numerical simulations of cosmological domain wall networks, in order to ensure a fixed comoving resolution. In this paper we explicitly demonstrate that the PRS algorithm provides the correct domain wall dynamics in ($N+1$)-dimensional Friedmann-Robertson-Walker universes if $\ensuremath{\alpha}+\ensuremath{\beta}/2=N$, fully validating its use in numerical studies of cosmic domain evolution. We further show that this result is valid for generic thin featureless domain walls, independently of the Lagrangian of the model.

Inflation in a web

In a given path with multiple branches, in principle, it can be expected that there are some fork points, where one branch is bifurcated into different branches, or various branches converge into one or several branches. In this paper, it is shown that if there is a web formed by such branches in a given field space, in which each branch can be responsible for a period of slow roll inflation, a multiverse separated by a domain wall network will come into being, some of which might correspond to our observable universe. We discuss this scenario and show possible observations of a given observer at late time.

The role of domain wall junctions in Carter's pentahedral model

The role of domain wall junctions in Carter's pentahedral model is investigated both analytically and numerically. We perform, for the first time, field theory simulations of such model with various initial conditions. We confirm that there are very specific realizations of Carter's model corresponding to square lattice configurations with X-type junctions which could be stable. However, we show that more realistic realizations, consistent with causality constraints, do lead to a scaling domain wall network with Y-type junctions. We determine the network properties and discuss the corresponding cosmological implications, in particular for dark energy.

Formation and evolution of kinky vortons

We present field theory simulations of a model with ℤ2 × U(1) symmetry in (2+1)-dimensions. This model has two discrete vacua, allowing for domain walls, and also a conserved Noether charge. For initial conditions in which the field is placed randomly in one of the vacua and given a homogeneous background charge, we find that the number of walls does not scale in the standard way. We argue that the Noether charge and current become localized on the walls, forming kinky vortons, (2+1)-dimensional analogues of cosmic vortons. These loops of wall can be long lived, or even stable, depending on their precise characteristics. We suggest that our simulations illustrate a possible mechanism for dynamical frustration of domain wall networks and that cosmic vortons will form naturally in U(1) × U(1) models.

Two-dimensional electron gas formed on the indium-adsorbedSi(111)3×3-Ausurface

Electronic structure of the In-adsorbed $\text{Si}(111)\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\text{-Au}$ surface was investigated by core-level and angle-resolved photoelectron spectroscopy. On the $\text{Si}(111)\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\text{-Au}$ surface, In adsorbates were reported to remove the characteristic domain-wall network and produce a very well-ordered $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ surface phase. Detailed band dispersions and Fermi surfaces were mapped for the pristine and In-dosed $\text{Si}(111)\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\text{-Au}$ surfaces. After the In adsorption, the surface bands shift toward a higher binding energy, increasing substantially the electron filling of the metallic band along with a significant sharpening of the spectral features. The resulting Fermi surface indicates the formation of a perfect isotropic two-dimensional electron-gas system filled with 0.3 electrons. This band structure agrees well with that expected, in a recent density-functional theory calculation, for the conjugate-honeycomb trimer model of the pristine $\text{Si}(111)\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\text{-Au}$ surface. Core-level spectra indicate that In adsorbates interact mostly with Si surface atoms. The possible origins of the electronic structure modification by In adsorbates are discussed. The importance of the domain wall and the indirect role of In adsorbates are emphasized. This system provides an interesting playground for the study of two-dimensional electron gas on solid surfaces.

Bifurcation and pattern changing with two real scalar fields

This work deals with bifurcation and pattern changing in models described by two real scalar fields. We consider generic models with quartic potentials and show that the number of independent polynomial coefficients affecting the ratios between the various domain wall tensions can be reduced to 4 if the model has a superpotential. We then study specific one-parameter families of models and compute the wall tensions associated with both Bogomol'nyi-Prasad-Sommerfield (BPS) and non-BPS sectors. We show how bifurcation can be associated to modification of the patterns of domain wall networks and illustrate this with some examples which may be relevant to describe realistic situations of current interest in high energy physics. In particular, we discuss a simple solution to the cosmological domain wall problem.

Dynamics of domain wall networks with junctions

We use a combination of analytic tools and an extensive set of the largest and most accurate three-dimensional field theory numerical simulations to study the dynamics of domain wall networks with junctions. We build upon our previous work and consider a class of models which, in the limit of large number $N$ of coupled scalar fields, approaches the so-called ``ideal'' model (in terms of its potential to lead to network frustration). We consider values of $N$ between $N=2$ and $N=20$, and a range of cosmological epochs, and we also compare this class of models with other toy models used in the past. In all cases we find compelling evidence for a gradual approach to scaling, strongly supporting our no-frustration conjecture. We also discuss the various possible types of junctions (including cases where there is a hierarchy of them) and their roles in the dynamics of the network. Finally, we provide a cosmological Zel'dovich-type bound on the energy scale of this kind of defect network: it must be lower than 10 keV.

Simulation of the spinodal phase separation dynamics of the Bi–Zn system

Abstract In the phase separation occurring at the miscibility gap (at the spinodal region) of an alloy a discrete symmetry is spontaneously broken and a domain wall network is formed. Field theory simulations are often used to study the dynamics of topological defects networks appearing in different physical contexts. In this work, we focus on the dynamics of the two immiscible liquids appearing on the phase diagram of the Bi–Zn system, one of the basic systems of lead free solders. We use phase field simulations to quantitatively simulate the dynamics of the two liquids separation in the Bi–Zn system, at different temperatures and for different concentrations. We obtain the miscibility gap curve and the domain morphologies of the system as a function of time, temperature and component concentrations using simulations.

Dynamics of domain walls for split and runaway potentials

We demonstrate that the evolution of wall-like inhomogeneities in runaway potentials, characteristic of dynamical supersymmetry breaking and moduli stabilization, is very similar to the evolution of domain-wall networks associated with double-well potentials. Instabilities that would lead to a rapid decay of domain walls can be significantly ameliorated by compensation effects between a nondegeneracy of the vacua and a biased initial distribution, which can be naturally expected in a wide class or particle physics models that lead to out-of-equilibrium phase transitions. Within this framework, it is possible to obtain domain walls that live long enough to be relevant for the cosmic power spectrum and galaxy clustering, while being compatible with the observed cosmic microwave background anisotropies.

Oscillons and domain walls

Oscillons, extremely long-lived localized oscillations of a scalar field, are shown to be produced by evolving domain wall networks in phi(4) theory in two spatial dimensions. We study the oscillons in frequency space using the classical spectral function at zero momentum, and obtain that the velocity distribution is suppressed as gamma(-2) at large Lorentz factor gamma, with oscillons produced up to at least gamma similar to 10. This leads us to speculate that oscillons are produced at cusps, regions of the domain wall travelling near the speed of light. In order to gain some insight onto the dilute oscillon produced by the domain walls, we prepare a denser gas by filling the simulation volume with oscillons boosted in random directions. We finish the study by revisiting collisions between oscillons and between an oscillon and a domain wall, showing that in the latter case they can pass straight through with minimal distortion.

Dynamics of domain wall networks

Networks or webs of domain walls are admitted in Abelian or non-Abelian gauge theory coupled to fundamental Higgs fields with complex masses. We examine the dynamics of the domain wall loops by using the moduli approximation and find a phase rotation induces a repulsive force which can be understood as a Noether charge of $Q$-solitons. Non-Abelian gauge theory allows different types of loops which can be deformed to each other by changing a modulus. This admits the moduli geometry like a sandglass made by gluing the tips of the two cigar-(cone-)like metrics of a single triangle loop. We conclude that the sizes of all loops tend to grow for a late time in general models with complex Higgs masses, while the sizes are stabilized at some values once triplet masses are introduced for the Higgs fields. We also show that the stationary motion on the moduli space of the domain wall webs represents $1/4$ Bogomol'nyi-Prasad-Sommerfield $Q$-webs of walls.

Branes and black holes in collision

We study the collision of a brane with a black hole. Our aim is to explore the topology changing process of perforation of a brane. The brane is described as a field theoretical domain wall in the context of an axionlike model consisting of a complex scalar effective field theory with approximate $U(1)$ symmetry. We simulate numerically the dynamics of the collision and illustrate the transition from the configuration without a hole to the pierced one with the aid of a phase diagram. The process of perforation is found to depend on the collisional velocity, and, contrary to our expectation, we observe that above a critical value of the velocity, the black hole has no chance to perforate the wall. That is: high energy collisions do not assist piercing. We also show that, only when the model parameters are fine-tuned so that the energy scale of the string is very close to that of the domain wall, the collision of the wall with the black hole has a possibility to provide a mechanism to erase domain walls, if the hole expands. However, in such cases, domain walls will form with many holes edged by a string and therefore disappear eventually. Therefore this mechanism is unlikely to be a solution to the cosmological domain wall problem, although it may cause some minor effects on the evolution of a domain wall network.

Properties of domain walls and magnetoresistance in low-doped La2−y SryCuO4

The properties of the diagonal stripe structures of the Hubbard model are theoretically studied in relation to the incommensurate spin order and the magnetic effects detected in the dielectric phase of low-doped La2−ySryCuO4 (y ≤ 0.05). The mean-field approximation is used to investigate the properties of the solutions with domain walls between antiphase antiferromagnetic domains that are centered on bonds. Such periodic structures with 2l sites in a unit cell are shown to have 2(l − 1) levels in the lower and upper Hubbard subbands and two levels that are separated into the Hubbard gap and correspond to quasi-one-dimensional states localized on domain walls. The calculation results are employed to check the assumption that the low conduction of the dielectric LSCO phase occurs via the network of domain walls. The maximum relative change in the magnetoresistance during a spin-flop transition in a critical magnetic field is estimated, and the giant magnetoresistance is qualitatively explained.