Super long-range kinks

TL;DR

This paper explores scalar field models with kink solutions exhibiting super long-range logarithmic tails, presenting analytical solutions, stability analysis, and methods to modify the range of these structures.

Contribution

It introduces models with null derivatives at minima, analytical solutions with logarithmic decay, and a formalism to transition between different long-range behaviors.

Findings

Analytical solutions with logarithmic tails are derived.

Super long-range structures are shown to be stable.

Methods to compare forces between super long-range kinks are presented.

Abstract

In this work we investigate the presence of scalar field models supporting kink solutions with logarithmic tails, which we call super long-range structures. We first consider models with a single real scalar field and associate the long-range profile to the orders of vanishing derivatives of the potential at its minima. We then present a model whose derivatives are null in all orders and obtain analytical solutions with logarithmic falloff. We also show that these solutions are stable under small fluctuations. To investigate the forces between super long-range structures, we consider three methods and compare them. Next, we study two-field models in which the additional field is used to modify the kinetic term of the other. By using a first-order formalism based on the minimization of the energy, we explore the situation in which one of the fields can be obtained independently from the other. Within this framework, we unveil how to smoothly go from long- or short- to super long-range structures.