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Comment to "Critical Exponents of the Superfluid-Bose Glass Transition in Three-Dimensions" by Z. Yao et al., arXiv:1402.5417v1

In this comment we address the preprint Z. Yao et al. (arXiv:1402.5417v1) concerning the conditions upon which the correct critical temperature exponent $ϕ$ can be observed (experimentally or numerically) close to the superfluid-Bose glass quantum phase transition in three dimensions. Yao et al. announce to have resolved the contradiction between the predictions of Fisher et al. [Phys. Rev. B 40, 546 (1989)] that $ϕ= νz \geq 2$ (where $ν$ and $z$ are critical exponents at the quantum phase transition) and recent experiments and simulations, showing an exponent $ϕ\sim 1.1$. Yao et al's resolution hinges on claiming that the $ϕ\sim 1.1$ observations, which were conducted by varying the chemical potential, were not made to sufficiently close to the critical point to observe universal behavior. Here we critically examine their criteria for observing universal behavior. We show that past simulations were in fact conducted closer to the quantum critical point than the new results of Yao et al.; and that Yao et al.'s own results for varying chemical potential are consistent with previous results showing $ϕ\sim 1.1$, and do not show a clear crossover to a different $ϕ$ value.