Short-time critical dynamics at perfect and imperfect surfaces

With Monte Carlo simulations, we study the dynamic relaxation at perfect and imperfect surfaces of the three-dimensional Ising model with an ordered initial state. The time evolution of the surface magnetization, the line magnetization of the defect line, and the corresponding susceptibilities and second cumulants is carefully examined. Universal dynamic scaling forms including a dynamic crossover scaling form are identified at the ordinary, special, and surface phase transitions. The critical exponents β₁ of the surface magnetization and β₂ of the line magnetization are extracted. The impact of the defect line on the universality classes is investigated.