  We investigate spectral functions in the vicinity of the critical temperature
of a second-order phase transition. Since critical phenomena in quantum field
theories are governed by classical dynamics, universal properties can be
computed using real-time lattice simulations. For the example of a relativistic
single-component scalar field theory in 2+1 dimensions, we compute the spectral
function described by universal scaling functions and extract the dynamic
critical exponent z. Together with exactly known static properties of this
theory, we obtain a verification from first principles that the relativistic
theory is well described by the dynamic universality class of relaxational
models with conserved density (Model C).
