Kink-kink and kink-antikink interactions with long-range tails

Abstract

In this Letter, we address the {long-range interaction} between kinks and antikinks, as well as kinks and kinks, in ${\phi }^{2n+4}$ field theories for $n>1$. The kink-antikink interaction is generically attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the $(\frac{2n}{n-1})$th power of their separation, and we identify the general prefactor for {\it arbitrary} $n$. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory and numerics for the cases of $n=2$ (${\phi }^8$ model), $n=3$ (${\phi }^{10}$ model) and $n=4$ (${\phi }^{12}$ model).

6 pages, 3 figures, revtex4-1 class; v2 includes minor revisions; v3 corrects typos, accepted for publication in Physical Review Letters