  It is a salient experimental fact that a large fraction of candidate spin
liquid materials freeze as the temperature is lowered. The question naturally
arises whether such freezing is intrinsic to the spin liquid ("disorder-free
glassiness") or extrinsic, in the sense that a topological phase simply
coexists with standard freezing of impurities. Here, we demonstrate a
surprising third alternative, namely that freezing and topological liquidity
are inseparably linked. The topological phase reacts to the introduction of
disorder by generating degrees of freedom of a new type (along with
interactions between them), which in turn undergo a freezing transition while
the topological phase supporting them remains intact.
