Renormalization-Group Approach to the Critical Behavior of Random-Spin Models

A renormalization-group technique is used to study the critical behavior of spin models in which each interaction has a small independent random width about its average value. The cluster approximation of Niemeyer and Van Leeuwen indicates that the two-dimensional Ising model has the same critical behavior as the homogeneous system. The ε expansion for n-component continuous spins shows that this behavior holds to first order in ε for $n>4$. For $n<4$, there is a new stable fixed point with 2ν=1+[3n16(n-1)]ε.