Fixed-Point Hamiltonian for a Randomly Driven Diffusive System

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Abstract
We consider the universal behavior of a system of interacting particles, diffusing under the influence of thermal noise and a random external field which drives the system into a non-equilibrium steady state. Critical exponents, distinct from both the Ising model and the uniformly driven system, are computed to two-loop order in an expansion around the upper critical dimension dc = 3. Our key result consists in the discovery of an effective, long-ranged Hamiltonian, formally identical to the one describing the critical behavior of uniaxial ferromagnets with dipolar interactions, which controls the time-independent, universal aspects of our far-from-equilibrium dynamics at the fixed point.

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