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

Abstract

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 $\epsilon$ expansion for $n$-component continuous spins shows that this behavior holds to first order in $\epsilon$ for $n>\mathrm{}4\mathrm{}$. For $n<\mathrm{}4\mathrm{}$, there is a new stable fixed point with $2\nu =1+\left[\frac{3n}{16(n-1\mathrm{})\mathrm{}}\right]\epsilon$.