ISING-MODEL ABOVE THE UPPER CRITICAL DIMENSION - AN APPLICATION TO BIOLOGY

We propose a spin model for idiotypic-anti-idiotypic immunological networks in which each spin interacts with its mirror-image spin and the neighbors of the image. We show that the critical properties of this model belong to the universality class of the Ising model, and that self-organizations, large homogeneous domains formed in the biological systems, are equivalent to spinodal decomposition. Since an immunological model has to be a 5-10 dimensional space for realistically representing the shape space, the space of all possible cell configurations, this represents the first application of an Ising model above its upper critical dimension d(u)=4.