Field theory of self-organized fractal etching

We propose a phenomenological field theoretical approach to the chemical etching of a disordered solid. The theory is based on a recently proposed dynamical etching model. Through the introduction of a set of Langevin equations for the model evolution, we are able to map the problem into a field theory related to isotropic percolation. To the best of the author's knowledge, this constitutes the first application of field theory to a problem of chemical dynamics. By using this mapping, many of the etching process critical properties are seen to be describable in terms of the percolation renormalization group fixed point. The emerging field theory has the peculiarity of being self-organized in the sense that without any parameter fine tuning the system develops fractal properties up to a certain scale controlled solely by the volume V of the etching solution. In the limit V --> infinity the upper cutoff goes to infinity and the system becomes scale invariant. We present also a finite size scaling analysis and discuss the relation of this particular etching mechanism to gradient percolation. Finally, the possibility of considering this mechanism as a generic path to self-organized criticality is analyzed, with the characteristics of being closely related to a real physical system and therefore more directly accessible to experiments.