Field-theoretic approaches to interacting particle systems: Lecture I
Seminar Room 1, Newton Institute
It is explained how field-theoretic methods and the dynamic renormalization group (RG) can be applied to study the universal scaling properties of interacting particle systems far from thermal equilibrium that either undergo a continuous phase transition or display generic scale invariance It is described how the master equation for stochastic particle reaction processes can be mapped onto a field theory action. The RG is then employed to analyze the ensuing power laws in simple diffusion-limited annihilation reactions as well as generic continuous transitions from active to inactive, absorbing states, which are characterized by the power laws of (critical) directed percolation. Certain other important universality classes including dynamic percolation and parity-conserving branching and annihilating random walks are discussed, and some open issues are mentioned.