  We describe a search for renormalization group fixed points which control a
second-order quantum phase transition between a d_{x^2-y^2} superconductor and
some other superconducting ground state. Only a few candidate fixed points are
found. In the finite temperature quantum-critical region of some of these fixed
points, the fermion quasiparticle lifetime is very short and the spectral
function has an energy width of order k_B T near the Fermi points. Under the
same conditions, the thermal conductivity is infinite in the scaling limit. We
thus provide simple, explicit, examples of quantum theories in two dimensions
for which a purely fermionic quasiparticle description of transport is badly
violated.
