  In a recent manuscript, the discovery of a new phenomenon in glasses has been
reported: {\it glass paramagnetism}, that is the intrinsic magnetisation
developed by a substance that has failed to crystallise in a temperature quench
when placed in an external magnetic field. The field- ($H$) and especially the
temperature- ($T$) dependence of the intrinsic magnetisation
$M_{intr}=M_{intr}(H,T)$ is very unexpected, with broad peaks developing for
high $H/T$ and marked $T$- oscillations at fixed $H$ for intermediate-to-high
temperatures. In this work we present details on the samples, new data for
other glassy systems and especially the theoretical background that is capable
of explaining most of the experimental data. New phenomena are however emerging
from these data, for example a deviation from the Curie-like behaviour of the
magnetic susceptibility ($M_{intr}/H$ at low fields) due to the glassy
structure alone as well as evidence for new and intriguing quantum coherence
effects at the lowest temperatures.
