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

Abstract

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.

Exponentially generalized vortex

“…and the BPS energy is r) dr. (36) Again, considering expression (21), we conclude that the BPS energy of the model is…”

Aspects of Kink‐Like Structures in 2D Dilaton Gravity

“…As mentioned in ref. [54], DCC contemplates measuring the informational complexity of a localized field configuration. For a field configuration with energy (r), one describes the 2D wave modes decomposition by Fourier's transform:…”

“…As mentioned in ref. [54], DCC contemplates measuring the informational complexity of a localized field configuration. For a field configuration with energy $$\mathcal {E}(r)$$, one describes the 2D wave modes decomposition by Fourier's transform: $$$$\begin{align} \mathcal {F}({\bf k})=\frac{1}{\sqrt {2\pi }}\int \mathcal {E}(r)\text{e}^{i{\bf k}\cdot {\bf r}} d{\bf r} \end{align}$$$$…”

Differential configurational entropy for multi-field of the ϕ 6 theory

“…CE is an extension of Shannon's theory [39][40][41]. However, CE and its variants (differential configuration entropy and differential configuration complexity are applied to continuous systems and provide information about the stability of localized structures [25]. In other words, while Shannon's theory studies the hidden information in a random process [41], CE is interpreted as a theoretical measure of the stability of the localized structures [39,40,[42][43][44].…”

“…where a = n 2 , b = n 2 , c = n 2 + 1, and y = e (−x0±x) . Using (24) and (25), solutions for the field φ are obtained. In this case, the solutions of the field φ are…”