چکیده :
We study localization properties of disordered bosons and spins
in random fields at zero temperature. We focus on two representatives
of different symmetry classes, hard-core bosons (XY magnets)
and Ising magnets in random transverse fields, and contrast
their physical properties. We describe localization properties using
a locator expansion on general lattices. For 1d Ising chains, we
find non-analytic behavior of the localization length as a function
of energy at ω = 0, ξ−1(ω) = ξ−1(0) + A|ω|α, with α vanishing
at criticality. This contrasts with the much smoother behavior predicted
for XY magnets. We use these results to approach the ordering
transition on Bethe lattices of large connectivity K, which mimic
the limit of high dimensionality.