Shape of the clusters of a percolative system in the presence of tunneling bonds and a finite electric field

We consider a model correlated percolative system on a 2D square lattice with a finite electric field applied accross its two opposite sides. We study the shape of the clusters formed with the addition of a new kind of bond (we call them tunneling bonds) which respond only above a finite threshold voltage. As expected, the clusters do have an overall elongated shape in the-direction of the applied field. Intuitively, one expects the elongation (with the aspect ratio >1) to increased indefinitely with the field. But, in a previous study, we found the model to belong to the same universality clas in the limits of a zero and an infinite electric field. We explain this behavior by studying the change in these elongated shapes as a function of the applied voltage in finite size samples and find that actually the amount of elongation takes on a maximum value at a size (L)-dependent finite voltageV _m (L) and that asV thje overall deviation from isotropy in the field direction tends to zero (i.e., aspect ratio1) again.