  The prediction and observation of low-temperature universal thermal
conductivity in cuprates has served as a keystone of theoretical approaches to
the superconducting state, but recent measurements on underdoped samples show
strong violations of this apparently fundamental property of d-wave nodal
quasiparticles. Here, we show that the breakdown of universality may be
understood as the consequence of disorder-induced magnetic states in the
presence of increasing antiferromagnetic correlations in the underdoped state,
even as these same correlations protect the nodal low-energy density of states
in agreement with recent scanning tunneling experiments.
