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

We propose a spin model for idiotypic-anti-idiotypic immunological net works in which each spin interacts with its mirror-image spin and the neighbors of the image. We show that the critical properties of this m odel belong to the universality class of the Ising model, and that sel f-organizations, large homogeneous domains formed in the biological sy stems, are equivalent to spinodal decomposition. Since an immunologica l model has to be a 5-10 dimensional space for realistically represent ing the shape space, the space of all possible cell configurations, th is represents the first application of an Ising model above its upper critical dimension d(u)=4.