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