  We have studied the spin glass behaviour of non-superconducting
La$_{2-x}$Sr$_x$Cu$_{0.95}$Zn$_{0.05}$O$_4$ ($x=0.10-0.22$). As in the
superconducting analogues of these samples the spin glass transition
temperature $T_g$ decreases with increasing $x$, and vanishes at $x=0.19$. A
local enhancement in $T_g$ at $x=0.12$ is also observed and attributed to
stripe ordering. The disappearance of $T_g$ for $x\geq0.19$ is discussed in
terms of a quantum phase transition.
