Hot kinks and antikinks
Grant Lythe and Salman Habib

Kinks in stochastic partial differential equations are similar to kinks in a piece of rope: they move about but maintain their identity. At zero temperature, a kink in classical Ø4 field theory joins -1 to +1 and an antikink joins +1 to -1. At non-zero temperature such objects are continuously being born (always in pairs) and moving about diffusively. When a kink meets an anti-kink, they both die.

It is now possible to run computer simulations that have enough points for a healthly population of kinks and anti-kinks, while keeping the points closely spaced enough to resolve kinks well. Below is one small part of a configuration from a simulation on 131072 points; each black dot is a grid point. We use a cooling algorithm to produce the solid line shown and thus identify the positions of kinks and antikinks at each time.

We next construct space-time diagrams like the one used as a background. Space is left-to-right and the direction of time is up the page; kinks paths are in in red and antikinks paths in green. A kink typically dies with the same antikink it was born with, but unfaithful kinks have long lifetimes.