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A pair of recent Monte Carlo studies have reported evidence for and against acrossover from weak to strong-disorder criticality in the one-dimensional dirtyboson problem. The Monte Carlo analyses rely on measurement of two observables:the effective Luttinger parameter K_{eff} and the superfluid susceptibilitychi. The former quantity was previously calculated analytically, using thestrong-disorder renormalization group (SDRG), by Altman, Kafri, Polkovnikov,and Refael. Here, we use an extension of the SDRG framework to find anon-universal anomalous dimension eta_{sd} characterizing the divergence of thesusceptibility with system size: chi ~ L^(2-eta_{sd}). We show that eta_{sd}obeys the hyperscaling relation eta_{sd} = 1/2K_{eff}. We also identify animportant obstacle to measuring this exponent on finite-size systems andcomment on the implications for numerics and experiments.

Susceptibility at the Superfluid-Insulator Transition for One-Dimensional Disordered Bosons