From thin to thick domain walls: An example of the $\varphi^8$ model

TL;DR

This paper explores explicit solutions for kinks in the $(1+1)$-dimensional $^8$ model, revealing conditions for thin and thick domain walls, with potential implications for cosmology.

Contribution

It provides explicit polynomial solutions for kinks in the $^8$ model and analyzes the transition from thin to thick domain walls in specific parameter regimes.

Findings

Explicit formulas for kinks in all topological sectors.

Identification of conditions leading to power-law asymptotics.

Thick domain walls modeled as kinks with power-law tails.

Abstract

We demonstrate that for some certain values of parameters of the $(1+1)$-dimensional $\varphi^8$ model, the kink solutions can be found from polynomial equations. For some selected values of the parameters we give the explicit formulas for the kinks in all topological sectors of the model. Based on the obtained algebraic equations, we show that in a special limiting case, kinks with power-law asymptotics arise in the model, describing, in particular, thick domain walls. Objects of this kind could be of interest for modern cosmology.