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.