Magnetic Eden Model

We introduce the "Magnetic Eden Model(s)". It consists in the usual Eden growth model(s), but allowing for the elements of the growth to have an extra degree of freedom (a "spin"). The growth is controlled by a condition depending on the "magnetic state" of the perimeter (through some "spin coupling") and an external parameter, the "magnetic field". Even though these words seem to refer to some "energetic condition" the growth model is of purely kinetic origin. This is demonstrated by exactly solving the 1-dimensional growth model for a semi-open chain, and, e.g. , finding the correlation functions. In two-dimensions, simulations of clusters lead us to show that the perimeter growth exponent is coupling dependent. We show the morphologies of growth clusters on a "phase diagram" and indicate the "physical origin" and transition(s) between compact and lacunar clusters.