Relevance ofφ4operators in the Edwards-Anderson model

Field-theoretical formulations of the spin-glass problem possess a symmetry which permits an invariant interaction of third order in the fluctuating fields. In the renormalization-group program one is naturally led to look for infrared-stable fixed points which yield $\epsilon$ expansions in $d=6-\epsilon$ dimensions. Naive dimensional analysis suggests that quartic interactions will become relevant in four dimensions, hence, precluding the use of $\epsilon$-expansion techniques to describe physics in three dimensions. We show that indeed the anomalous dimensions of quartic operators are such that for Ising and $X-Y$ systems and $\epsilon$ expansion around six dimensions should not be extrapolated down to three dimensions. However, for a Heisenberg system the quartic interactions remain irrelevant.