Toward A Mean Field Model of a Genome

Mean eld spin glass models with synchronous dynamics, asymmetric random bonds, and p-spin ferromagnetic interactions are explored at their critical points as possible models for genetic regulatory networks. The numbers of xed points are found to scale like N 1=3 and N 1=4 for two universality classes identiied among these models. There are also numbers of n-cycles of the same order for n N 1=5 and n N 1=4 for the two classes, respectively.