Critical behavior of linearΦ4models withG×G′symmetry

Abstract

The critical behavior of ${\Phi }^4$ theories with global symmetry $O\left(N\right)\mathrm{}\times O\left(M\right)\mathrm{}$ and $U\left(N\right)\mathrm{}\times U\left(M\right)\mathrm{}$ is investigated to one-loop order in $4-\epsilon$ dimensions. For many values of $N$ and $M$, no infrared stable fixed point exists. In both cases, an infrared stable fixed point exists when $N=M=0\mathrm{}$; this limit is relevant to self-interacting, double-stranded polymers.