  We formulate a strong-disorder renormalization-group (SDRG) approach to study
the beta function of the tight-binding model in one dimension with both
diagonal and off-diagonal disorder for states at the band center. We show that
the SDRG method, when used to compute transport properties, yields exact
results since it is identical to the transfer matrix method. The beta function
is shown to be universal when only off-diagonal disorder is present even though
single-parameter scaling is known to be violated. A different single-parameter
scaling theory is formulated for this particular (particle-hole symmetric)
case. Upon breaking particle-hole symmetry (by adding diagonal disorder), the
beta function is shown to crossover from the universal behavior of the
particle-hole symmetric case to the conventional non-universal one in agreement
with the two-parameter scaling theory. We finally draw an analogy with the
random transverse-field Ising chain in the paramagnetic phase. The
particle-hole symmetric case corresponds to the critical point of the quantum
Ising model while the generic case corresponds to the Griffiths paramagnetic
phase.
