Topological defects with power-law tails

TL;DR

This paper investigates the interactions of kinks and antikinks with mixed tail asymptotics in a $ ext{phi}^8$ model, revealing that their forces decay slowly as a power law, with numerical and analytical estimates supporting this behavior.

Contribution

It introduces the study of kink-antikink interactions with mixed power-law and exponential tails, providing both numerical and analytical estimates of the interaction force.

Findings

Interaction force decays as a negative power of distance

Numerical estimates align with analytical predictions

Kinks with mixed tail asymptotics exhibit slow decay of interaction force

Abstract

We study interactions of kinks and antikinks of the $(1+1)$-dimensional $\varphi^8$ model. In this model, there are kinks with mixed tail asymptotics: power-law behavior at one infinity versus exponential decay towards the other. We show that if a kink and an antikink face each other in way such that their power-law tails determine the kink--antikink interaction, then the force of their interaction decays slowly, as some negative power of distance between them. We estimate the force numerically using the collective coordinate approximation, and analytically via Manton's method (making use of formulas derived for the kink and antikink tail asymptotics).