Interaction between kinks and antikinks with double long-range tails

We explore a class of phi(4n) models with kink and antikink solutions that have long-range tails on both sides, specializing to the cases with n = 2 and n = 3. A recently developed method of an accelerating kink ansatz is used to estimate the force between the kink and the antikink. We use state-of-the-art numerical methods to initialize the system in a kink-antikink configuration with a finite initial velocity and to evolve the system according to the equations of motion. Among these methods, we propose a computationally efficient way to initialize the velocity field of the system. Interestingly, we discover that, for this class of models, phi(4n) with n > 1, the kink-antikink annihilation behaves differently from the archetypal phi(4) model or even the kinks with one long-range tail because there is neither long-lived bion formation nor resonance windows and the critical velocity is ultrarelativistic. (C) 2021 The Authors. Published by Elsevier B.V.

Automated summary

In this work, a class of phi(4n) models with long-range tails on both sides is explored, focusing on the cases with n = 2 and n = 3. The study reveals that for models with n > 1, the kink-antikink annihilation behavior differs from the phi(4) model and kinks with one long-range tail, showing an ultrarelativistic critical velocity.