Kinks in the relativistic model with logarithmic nonlinearity

Belendryasova, Ekaterina; Gani, Vakhid A.; Zloshchastiev, Konstantin G.

doi:10.1088/1742-6596/1390/1/012082

Cited by 10 publications

(10 citation statements)

References 43 publications

(56 reference statements)

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“…We started our investigation considering a Lagrangian density in flat space-time in (2 + 1)D as proposed in Refs. [7,29], given by…”

Section: The Gauged O(3)-sigma Model With Chern-simons Termmentioning

confidence: 99%

“…In this work, we will introduce for the first time a logarithmic potential in the O(3)sigma model context. It is known that a logarithmic potential generates solitonic solutions in bidimensional models with logarithmic nonlinearity [29]. Recently, it has been observed that the logarithmic potential can generate ring-like vortices with intense magnetic flux when the Higgs field is coupled to the gauge field [30].…”

Section: Introductionmentioning

confidence: 99%

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Differential configurational complexity and phase transitions of the BPS solutions in the O(3)-sigma model

Lima,

Almeida

2022

Preprint

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Using a spherically symmetric ansatz, we show that the Chern-Simons O(3) -sigma model with a logarithmic potential admits topological solutions. This result is quite interesting since the Gausson-type logarithmic potential only predicted topological solutions in (1 + 1)D models. To accomplish our goal, the Bogomol'nyi-Prasad-Sommerfield (BPS) method is used, to saturate the energy and obtain the BPS equations. Next, we show by numerical method the graphical results of the topological fields, as well as, the magnetic field behavior that generates a flux given by Φ f lux = −Q/κ and the energy density of the structures of vortices. On the other hand, we evaluate the measure of the differential configurational complexity (DCC) of the topological structures, by considering the energy density of the vortex. This analysis is important because it will provide us with information about the possible phase transitions associated with the localized structures and it shows that our model only supports one phase transition.

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“…We started our investigation considering a Lagrangian density in flat space-time in (2 + 1)D as proposed in Refs. [7,29], given by…”

Section: The Gauged O(3)-sigma Model With Chern-simons Termmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Differential configurational complexity and phase transitions of the BPS solutions in the O(3)-sigma model

Lima,

Almeida

2022

Preprint

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“…We know that at ε = 0, one has Σ = µ 2 |∂φ| , and substituting this result to the equations of motion in ε = 0 case, one recovers the initial cuscuton action (1). The Σ 1 is a first-order approximation to be found: implementing the expansion (45) into the equation of motion (44), one obtains, in the first order in ε, that Σ 1 = m 4 µ 4 . Thus, we substituite Σ = µ 2 |∂φ| + ε m 4 µ 4…”

Section: Comments On Perturbative Dynamics Of the Cuscutonmentioning

confidence: 99%

Topological structures in a non-canonical perturbative dynamics of a cuscuton-like model

Lima,

Petrov,

Almeida

2021

Preprint

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In this work, a possible description for quantum dynamics of the cuscuton within the sigma-model approach is presented. Lower order perturbative corrections and the structure of divergences are found. Motivated by the results generated by the perturbative approach, we investigate the existence of topological structures in the cuscuton-like model. The structures we study are, first, kink-like configurations in two dimensional spacetime, second, vortex solutions in three dimensional one with gauge field ruled by the Maxwell term. In fact, to show the existence of kink solutions it is needed to introduce a standard dynamics term in the cuscuton-like model. Then, a numerical approach (interpolation method) is used and the solution of the scalar field is presented. On the other hand, for the study of topological vortices, we reorganized the energy density to obtain, for convenience, equations similar to those canonical vortex structures, namely, the Maxwell-Higgs model. In fact, even for this particular case, we observed the existence of structures with localized energy and quantized magnetic flux in a given topological sector. We also show that when the model does not spontaneously break the symmetry, the (2 + 1)D model only admits the so-called non-topological field solutions.

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“…This discussion has recently returned with the study of kinks generated by Gausson-like potentials in Ref. [35] and with generalized models using Gausson-like logarithmic terms in Refs. [36,37].…”

Section: Introductionmentioning

confidence: 99%

Phase transitions in the logarithmic Maxwell O(3)-sigma model

Lima

Almeida

2021

Eur. Phys. J. C

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We investigate the presence of topological structures and multiple phase transitions in the O(3)-sigma model with the gauge field governed by Maxwell’s term and subject to a so-called Gausson’s self-dual potential. To carry out this study, it is numerically shown that this model supports topological solutions in 3-dimensional spacetime. In fact, to obtain the topological solutions, we assume a spherically symmetrical ansatz to find the solutions, as well as some physical behaviors of the vortex, as energy and magnetic field. It is presented a planar view of the magnetic field as an interesting configuration of a ring-like profile. To calculate the differential configurational complexity (DCC) of structures, the spatial energy density of the vortex is used. In fact, the DCC is important because it provides us with information about the possible phase transitions associated with the structures located in the Maxwell–Gausson model in 3D. Finally, we note from the DCC profile an infinite set of kink-like solutions associated with the parameter that controls the vacuum expectation value.

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Kinks in the relativistic model with logarithmic nonlinearity

Cited by 10 publications

References 43 publications

Differential configurational complexity and phase transitions of the BPS solutions in the O(3)-sigma model

Differential configurational complexity and phase transitions of the BPS solutions in the O(3)-sigma model

Topological structures in a non-canonical perturbative dynamics of a cuscuton-like model

Phase transitions in the logarithmic Maxwell O(3)-sigma model

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