One-loop results for kink and domain wall profiles at zero and finite temperature

TL;DR

This paper analytically computes one-loop quantum and thermal corrections to kink and domain wall profiles in various dimensions, revealing effects like melting, interface roughening, and the need for renormalization of local energy distributions.

Contribution

It provides new analytical results for temperature-dependent kink profiles and domain wall properties, including infrared singularities and renormalization effects in higher dimensions.

Findings

Kinks melt as temperature approaches phase transition.

Infrared singularities indicate interface roughening.

Local energy density requires renormalization in 3+1 dimensions.

Abstract

Using dimensional regularization, we compute the one-loop quantum and thermal corrections to the profile of the bosonic 1+1-dimensional phi^4 kink, the sine-Gordon kink and the CP^1 kink, and higher-dimensional phi^4 kink domain walls. Starting from the Heisenberg field equation in the presence of the nontrivial kink background we derive analytically results for the temperature-dependent mean field which display the onset of the melting of kinks as the system is heated towards a symmetry restoring phase transition. The result is shown to simplify significantly when expressed in terms of a self-consistently defined thermal screening mass. In the case of domain walls, we find infrared singularities in the kink profile, which corresponds to interface roughening depending on the system size. Finally we calculate the energy density profile of phi^4 kink domain walls and find that in contrast to the total surface tension the local distribution requires composite operator renormalization in 3+1 dimensions.