Universal non-equilibrium scaling of cumulants across a critical point

We study the critical dynamics of a scalar field theory with $Z_2$ symmetry in the dynamic universality class of Model A in two and three spatial dimensions with classical-statistical lattice simulations. In particular, we measure the non-equilibrium behavior of the system under a quench protocol in which the symmetry-breaking external field is changed at a constant rate through the critical point. Using the well-established Kibble-Zurek scaling theory we compute non-equilibrium scaling functions of cumulants of the order parameter up to fourth order. Together with the static critical exponents and the dynamic critical exponent, these fully describe the universal non-equilibrium evolution of the system near the critical point. We further extend the analysis to include finite-size effects and observe good collapse of our data onto two-dimensional universal non-equilibrium and finite-size scaling functions.