Renormalized critical dynamics and fluctuations in model A in the Hohenberg-Halperin classification

In the context of relativistic heavy-ion collisions, we explore the stochastic and dissipative relaxational dynamics of a nonconserved order parameter in a $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ interaction. The cutoff of the theory is provided by the lattice spacing chosen for our numerical simulations. As a consequence, observables become dependent on that scale. We consider a possible first-order phase transition and an evolution close to a critical point. We demonstrate that using a lattice counterterm restores the expected behavior of the mean, variance, and kurtosis: the mean and the variance become lattice spacing independent, and we recover the correct expectation value of the mean, the growth of the variance with the correlation length, and the expected minimum in the kurtosis. Our findings hold true in equilibrium and during the dynamical relaxation, and therefore mark an important step towards a fully fluctuating fluid dynamical setup.