scholarly journals On the absence of spontaneous symmetry breaking and of crystalline ordering in two-dimensional systems

1981 ◽  
Vol 81 (2) ◽  
pp. 277-298 ◽  
Author(s):  
Jürg Fröhlich ◽  
Charles Pfister
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Two Dimensional

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 Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials

2011 ◽  
Vol 58 (21) ◽  
pp. 1977-1989 ◽  
Author(s):  
Thawatchai Mayteevarunyoo ◽  
Boris A. Malomed ◽  
Athikom Reoksabutr
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Two Dimensional ◽  
Matter Waves

scholarly journals Embedding cosmology and gravity

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Abhishek Goswami
Keyword(s):  
Field Theory ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Sigma Model ◽  
Two Dimensional ◽  
Abstract Space ◽  
Einstein's Equation ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Dimensional Surface

AbstractI start with a scenario where the universe is an abstract space $${\mathcal {M}}$$ M having d dimensions. There is a two dimensional surface embedded in it. Embedding is a map from the embedded surface to $${\mathcal {M}}$$ M that has a field theory described by Sigma model. I take d directions of $${\mathcal {M}}$$ M to be the generators of a symmetry group SU(n) of the Lagrangian of the embedding. This means embedding has n flavors. Then I introduce spontaneous symmetry breaking in the theory and define the direction along which the symmetry breaking occurs as time. Next I write down the modified Einstein’s equation including the embedding. Then I discuss embedding’s relation to the expansion of the universe. After that I construct an inflationary scenario with embedding as inflaton and discuss its connection to Starobinsky $$R^{2}$$ R 2 model. Finally, I discuss the effect of inflation on the non-commutativity of the spacetime.

scholarly journals Abelian and non-abelian symmetries in infinite projected entangled pair states

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Claudius Hubig
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Ground State ◽  
Heisenberg Model ◽  
Computational Effort ◽  
Square Lattice ◽  
Two Dimensional ◽  
Computational Speed ◽  
Speed Up ◽  
Ground State Energies

We explore in detail the implementation of arbitrary abelian and non-abelian symmetries in the setting of infinite projected entangled pair states on the two-dimensional square lattice. We observe a large computational speed-up; easily allowing bond dimensions D=10D=10 in the square lattice Heisenberg model at computational effort comparable to calculations at D=6D=6 without symmetries. We also find that implementing an unbroken symmetry does not negatively affect the representative power of the state and leads to identical or improved ground-state energies. Finally, we point out how to use symmetry implementations to detect spontaneous symmetry breaking.

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 Spontaneous Symmetry Breaking and Coherence in Two-Dimensional Electron–Hole and Exciton Systems

2012 ◽  
Vol 7 (7) ◽  
pp. 640-670 ◽  
Author(s):  
S. A. Moskalenko ◽  
M. A. Liberman ◽  
E. V. Dumanov ◽  
E. S. Moskalenko
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Electron Hole

Spontaneous symmetry breaking of a Bose—Fermi mixture in a two-dimensional double-well potential

2012 ◽  
Vol 21 (1) ◽  
pp. 010309 ◽  
Author(s):  
Yuan-Sheng Wang ◽  
Pei-Gen Yan ◽  
Bin Li ◽  
Xue-Shen Liu
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Two Dimensional ◽  
Double Well Potential
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