Do local field potentials (LFP) create waves on the surfaces of nerve cells?
A LFP can be measured at any point in space and is just the sum of all the fields generated by nearby charges.  Conventionally, it's assumed to be some distance from a cluster of neurons, but you technically could measure the LFP near the external surface of a neuron (but that would bias your signal towards the reading of that one neuron).  

LFP's are relatively weak, but have some small influence on the neighboring cells:

Modeling the coupling of single neuron activity to local field potentials