Noise indused transition in spatially heterogenious space

Noise induced phase transition is reported some kind of subjects in several research field. Most of them are focused on phase transition in homogeneous system. So, I'd like to expand it into heterogeneous system ( heterogeneous system means the system with spatial structure in this case, contrary, homogeneous system is no spatial expression.)

In my case, start with the system which have double well free energy structure to express phase stability and order parameter may interact 1st nearest neighbor in diffusional flow. In this case, I'd like to neglect long range interaction between local grid for simplicity. Next step is to create kind of noise generator to inducu noise into the system expressing above. So, I'm very interested in overlapping noisefield and phase transition field.

Tetsuya