  We focus on two real-space renormalization-group (RG) methods recently
proposed for a hierarchical model of a spin glass: A sample-by-sample method,
in which the RG transformation is performed separately on each disorder sample,
and an ensemble RG (ERG) method [M. C. Angelini, G. Parisi, and F.
Ricci-Tersenghi. Ensemble renormalization group for disordered systems.
$\textit{Phys. Rev. B}$, 87(13):134201, 2013] in which the transformation is
based on an average over samples. Above the upper critical dimension, the
sample-by-sample method yields the correct mean-field value for the critical
exponent $\nu$ related to the divergence of the correlation length, while it
does not predict the correct qualitative behavior of $\nu$ below the upper
critical dimension. On the other hand, the ERG procedure has been claimed to
predict the correct behavior of $\nu$ both above and below the upper critical
dimension. Here, we straighten out the reasons for the discrepancy between the
two methods above, by demonstrating that the ERG method predicts a marginally
stable critical fixed point, thus implying a prediction for the critical
exponent $\nu$ given by $2^{1/\nu} = 1$. This prediction disagrees, on a
qualitative and quantitative level, both with the mean-field value of $\nu$
above the critical dimension, and with numerical estimates of $\nu$ below the
upper critical dimension. Therefore, our results show that finding a real-space
RG method for spin glasses which yields the correct prediction for universal
quantities below the upper critical dimension is still an open problem, for
which our analysis may provide some general guidance for future studies.

Disordered Systems and Neural Networks;Statistical Mechanics