Abstract
We study interactions of kinks and antikinks of the (1 + 1)-dimensional ϕ8 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).
Highlights
Field-theoretic models with polynomial self-interaction are of growing interest in various areas of modern physics, from cosmology and high energy physics to condensed matter theory [1, 2, 3].In (1+1)-dimensional models of a real scalar field with a high-order polynomial self-interaction potential, there exist topological solutions of the type of kinks, which can possess tails such that either or both decay as power laws towards the asymptotic states connected by the kink [3, 4]
Properties of kinks with exponential tail asymptotics are well-understood [5, 6, 7, 8, 9, 10, 11, 12]
Within a specific φ8 model, we have shown that if a kink and an antikink interact via tails that decay as power-laws, a long-range interaction appears in the system — the force of the kink-antikink interaction decays much more slowly than in the (“usual”) case of exponentially decaying tails
Summary
Field-theoretic models with polynomial self-interaction are of growing interest in various areas of modern physics, from cosmology and high energy physics to condensed matter theory [1, 2, 3]. In (1+1)-dimensional models of a real scalar field with a high-order polynomial self-interaction potential, there exist topological solutions of the type of kinks, which can possess tails such that either or both decay as power laws towards the asymptotic states connected by the kink [3, 4]. We know a lot about kink-antikink interactions in such models. Interactions of kinks with power-law tails have not been studied in such detail. The study of some properties and interactions of plane domain walls in (2 + 1) and (3 + 1) dimensional worlds can often be reduced to studying the properties and interactions of kinks in (1 + 1) dimensions [13, 14, 15, 16, 17, 18]
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