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4cefc56f-d72a-458a-afb5-6a7ec3d9ba57
Jun 27 00:11:24 UTC
Can the number of dimensions in an effective theory depend on the lengthscale/energyscale where it is defined? In other words, can d be running due to RG flow?
e24f3a77-af85-4fca-8788-bf80b98a0758
Jul 2 20:03:42 UTC
For example, consider an elastic network. On the microscopic scale, it is one-dimensional. Due to branching, a fractal dimension greater 1 appears. On a large scale, what you see is no longer a linear segment but a space-filling structure whose fractal dimension is less than the embedding dimension. The elastic behaviour (normal modes, VDOS, Green's function etc.) should depend on this fractal dimension, which may change smoothly as you zoom out from the microscopic to the macroscopic scale, should it not?