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We present a new numerical Monte Carlo approach to determine the scalingbehavior of lattice field theories far from equilibrium. The presented methodsare generally applicable to systems where classical-statistical fluctuationsdominate the dynamics. As an example, these methods are applied to therandom-force-driven one-dimensional Burgers' equation - a model forhydrodynamic turbulence. For a self-similar forcing acting on all scales thesystem is driven to a nonequilibrium steady state characterized by a Kolmogorovenergy spectrum. We extract correlation functions of single- and multi-pointquantities and determine their scaling spectrum displaying anomalous scalingfor high-order moments. Varying the external forcing we are able to tune thesystem continuously from equilibrium, where the fluctuations are short-rangecorrelated, to the case where the system is strongly driven in the infrared. Inthe latter case the nonequilibrium scaling of small-scale fluctuations areshown to be universal.

Lattice Monte Carlo methods for systems far from equilibrium