Path integral evaluation of the one-loop effective potential in field theory of diffusion-limited reactions

Abstract

The well-established effective action and effective potential framework from the quantum field theory domain is adapted and successfully applied to classical field theories of the Doi and Peliti type for diffusion controlled reactions. Through a number of benchmark examples, we show that the direct calculation of the effective potential in fixed space dimension $d=2$ to one-loop order reduces to a small set of simple elementary functions, irrespective of the microscopic details of the specific model. Thus the technique, which allows one to obtain with little additional effort, the potentials for a wide variety of different models, represents an important alternative to the standard model dependent diagram-based calculations. The renormalized effective potential, effective equations of motion and the associated renormalization group equations are computed in $d=2$ spatial dimensions for a number of single species field theories of increasing complexity.

Plain LaTEX2e, 32 pages and three figures. Submitted to Journal of Statistical Physics

References in corpus (12)

• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Field Theory of Branching and Annihilating Random Walks
• Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
• `Real' vs `Imaginary' Noise in Diffusion-Limited Reactions
• Non Perturbative Renormalization Group study of reaction-diffusion processes and directed percolation
• Quantitative Phase Diagrams of Branching and Annihilating Random Walks
• Effective action for stochastic partial differential equations
• Extinction in population dynamics
• Phase diagram of aggregation of oppositely charged colloids in salty water
• Equation of state for directed percolation
• Comment on Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
• Renormalization Group Improving the Effective Action