Logarithmic correction to scaling in domain-wall dynamics at Kosterlitz-Thouless phase transitions.

With Monte Carlo simulations, we investigate the relaxation dynamics of domain walls at the Kosterlitz-Thouless phase transition, taking the two-dimensional $XY$ model as an example. The dynamic scaling behavior is carefully analyzed, and a domain-wall roughening process is observed. Two-time correlation functions are calculated and aging phenomena are investigated. Inside the domain interface, a strong logarithmic correction to scaling is detected.