Critical Exponents of the Superfluid-Bose Glass Transition in Three-Dimensions

Recent experimental and numerical studies of the critical-temperature exponent $\phi$ for the superfluid-Bose glass universality in three-dimensional systems report strong violations of the key quantum critical relation, $\phi=\nu z$, where $z$ and $\nu$ are the dynamic and correlation length exponents, respectively, and question the fundamental concepts underlying quantum critical phenomena. Using Monte Carlo simulations of the disordered Bose-Hubbard model, we demonstrate that previous work on the superfluid-to-normal fluid transition-temperature dependence on chemical potential (or magnetic field, in spin systems), $T_c \propto (\mu-\mu_c)^{\phi}$, was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the $\phi=\nu z$ law [with $\phi=2.7(2)$, $z=3$, and $\nu = 0.88(5)$] holds true, resolving the $\phi$-exponent "crisis".