  We present a new numerical Monte Carlo approach to determine the scaling
behavior of lattice field theories far from equilibrium. The presented methods
are generally applicable to systems where classical-statistical fluctuations
dominate the dynamics. As an example, these methods are applied to the
random-force-driven one-dimensional Burgers' equation - a model for
hydrodynamic turbulence. For a self-similar forcing acting on all scales the
system is driven to a nonequilibrium steady state characterized by a Kolmogorov
energy spectrum. We extract correlation functions of single- and multi-point
quantities and determine their scaling spectrum displaying anomalous scaling
for high-order moments. Varying the external forcing we are able to tune the
system continuously from equilibrium, where the fluctuations are short-range
correlated, to the case where the system is strongly driven in the infrared. In
the latter case the nonequilibrium scaling of small-scale fluctuations are
shown to be universal.
