scholarly journals Topological structures, spontaneous symmetry breaking and energy spectra in dipole hexagonal lattices

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Josep Batle
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Minimum Energy ◽  
Three Dimensional ◽  
Topological Defects ◽  
Dipole Interaction ◽  
Honeycomb Lattice ◽  
Two Dimensional ◽  
Topological Structures ◽  
Dipole Force

AbstractThe interplay between the special triangular/hexagonal two dimensional lattice and the long range dipole–dipole interaction gives rise to topological defects, specifically the vortex, formed by a particular arrangement of the interacting classic dipoles. The nature of such vortices has been traditionally explained on the basis of numerical evidence. Here we propose the emerging formation of vortices as the natural minimum energy configuration of interacting (in-plane) two-dimensional dipoles based on the mechanism of spontaneous symmetry breaking. As opposed to the quantal case, where spin textures such as skyrmions or bimerons occur due to non-linearities in their Hamiltonian, it is still possible to witness classic topological structures due only to the nature of the dipole–dipole force. We shall present other (new) topological structures for the in-plane honeycomb lattice, as well as for two-dimensional out-of-plane dipoles. These structures will prove to be essential in the minimum energy configurations for three-dimensional simple hexagonal and hexagonal-closed-packed structures, whose energies in the bulk are obtained for the first time.

scholarly journals Stability of Two-Dimensional Viscous Incompressible Flows under Three-Dimensional Perturbations and Inviscid Symmetry Breaking

2013 ◽  
Vol 45 (3) ◽  
pp. 1871-1885 ◽  
Author(s):  
C. Bardos ◽  
M. C. Lopes Filho ◽  
Dongjuan Niu ◽  
H. J. Nussenzveig Lopes ◽  
E. S. Titi
Keyword(s):  
Symmetry Breaking ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Viscous Incompressible Flows

scholarly journals Variance of Voltages in a Lattice Coulomb Gas

2021 ◽  
Vol 186 (1) ◽  
Author(s):  
Diana Conache ◽  
Markus Heydenreich ◽  
Franz Merkl ◽  
Silke W. W. Rolles
Keyword(s):  
High Temperature ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Temperature Regime ◽  
Gaussian Model ◽  
Coulomb Gas ◽  
Two Dimensional ◽  
Discrete Gaussian Model ◽  
Dimensional Lattice ◽  
The Difference

AbstractWe study the behavior of the variance of the difference of energies for putting an additional electric unit charge at two different locations in the two-dimensional lattice Coulomb gas in the high-temperature regime. For this, we exploit the duality between this model and a discrete Gaussian model. Our estimates follow from a spontaneous symmetry breaking in the latter model.

scholarly journals Formation of complex two-dimensional dissipative solitons via spontaneous symmetry breaking

2014 ◽  
Vol 90 (2) ◽  
Author(s):  
V. Skarka ◽  
N. B. Aleksić ◽  
M. Lekić ◽  
B. N. Aleksić ◽  
B. A. Malomed ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Two Dimensional ◽  
Dissipative Solitons

scholarly journals An introduction to spontaneous symmetry breaking

2019 ◽  
Author(s):  
Aron Beekman ◽  
Louk Rademaker ◽  
Jasper van Wezel
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Condensed Matter ◽  
Topological Defects ◽  
High Energy ◽  
Quantum Corrections ◽  
Gauge Fields ◽  
Singular Limits ◽  
Definition Of ◽  
Goldstone Modes

Perhaps the most important aspect of symmetry in physics is the idea that a state does not need to have the same symmetries as the theory that describes it. This phenomenon is known as spontaneous symmetry breaking. In these lecture notes, starting from a careful definition of symmetry in physics, we introduce symmetry breaking and its consequences. Emphasis is placed on the physics of singular limits, showing the reality of symmetry breaking even in small-sized systems. Topics covered include Nambu-Goldstone modes, quantum corrections, phase transitions, topological defects and gauge fields. We provide many examples from both high energy and condensed matter physics. These notes are suitable for graduate students.

scholarly journals ON THE SYMMETRY OF THE VACUUM IN THEORIES WITH "SPONTANEOUS SYMMETRY BREAKING"

2011 ◽  
Vol 26 (09) ◽  
pp. 1493-1544 ◽  
Author(s):  
ALEJANDRO PEREZ ◽  
DANIEL SUDARSKY
Keyword(s):  
Field Theory ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Topological Defects ◽  
Quantum Field ◽  
Mass Generation ◽  
Symmetric Scheme ◽  
Gauge Symmetries ◽  
Symmetric Vacuum ◽  
The Common

We review the usual account of the phenomena of spontaneous symmetry breaking, pointing out the common misunderstandings surrounding the issue, in particular within the context of quantum field theory. In fact, the common explanations one finds in this context, indicate that under certain conditions corresponding to the situation called spontaneous symmetry breaking, the vacuum of the theory does not share the symmetries of the Lagrangian. We explain in detail why this statement is incorrect in general, and in what limited set of circumstances such a situation could arise. We concentrate on the case of global symmetries, for which we found no satisfactory exposition in the existing literature, and briefly comment on the case of gauge symmetries where, although insufficiently publicized, accurate and complete descriptions exist. We briefly discuss the implications for the phenomenological manifestations usually attributed to the phenomena of spontaneous symmetry breaking, analyzing which might be affected by our analysis and which are not. In particular we describe the mass generation mechanism in a fully symmetric scheme (i.e. with a totally symmetric vacuum), and briefly discuss the implications of this analysis to the problem of formation of topological defects in the early universe.

scholarly journals Interconversion of multiferroic domains and domain walls

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
E. Hassanpour ◽  
M. C. Weber ◽  
Y. Zemp ◽  
L. Kuerten ◽  
A. Bortis ◽  
...  
Keyword(s):  
Domain Wall ◽  
Physical Properties ◽  
Domain Walls ◽  
Three Dimensional ◽  
Topological Defects ◽  
Long Range Order ◽  
Two Dimensional ◽  
Domain Structures ◽  
Topological Singularities ◽  
Ordered State

AbstractSystems with long-range order like ferromagnetism or ferroelectricity exhibit uniform, yet differently oriented three-dimensional regions called domains that are separated by two-dimensional topological defects termed domain walls. A change of the ordered state across a domain wall can lead to local non-bulk physical properties such as enhanced conductance or the promotion of unusual phases. Although highly desirable, controlled transfer of these properties between the bulk and the spatially confined walls is usually not possible. Here, we demonstrate this crossover by confining multiferroic Dy0.7Tb0.3FeO3 domains into multiferroic domain walls at an identified location within a non-multiferroic environment. This process is fully reversible; an applied magnetic or electric field controls the transformation. Aside from expanding the concept of multiferroic order, such interconversion can be key to addressing antiferromagnetic domain structures and topological singularities.

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