Simulations of the immunological shape space: Influence of the interaction range in an Ising-like Model

Stauffer(7) has replaced the window automata rules - applied by de Beer, Segel and Perelson(2) for simulating the immunological shape space - by probabilistic rules, very similar to the ones of the ferromagnetic Ising Model. Based on this model, we extend the interaction range to more than nearest neighbors and find phase transitions not only in higher dimensions, but also in two dimensions. Biologically these phase transitions correspond to a transition from a reasonable to a non-reasonable behavior of the whole immune network.