Phonon-induced modification of quantum criticality

We study the effect of acoustic phonons on the quantum phase transition in the O(N) model. We develop a renormalization group (RG) analysis near (3+1) space-time dimensions and derive the RG equations using an ϵ expansion. Our results indicate that when the number of flavors of the underlying O(N) model exceeds a critical number Nc=4, the quantum transition remains second-order of the Wilson-Fisher type while, for N≤4, it is a weakly first-order transition. We characterize this weakly first-order transition by a length scale ζ∗, below which the behavior appears to be critical. At finite temperatures for N≤4, a tricritical point separates the weakly first-order and second-order transitions.