  We study the decoherence of a spin-1/2 induced by an environment which is on
the verge of a continuous phase transition. We consider spin environments
described by the ferromagnetic and antiferromagnetic Heisenberg models on a
square lattice. As is well known, these two dimensional systems undergo a
continuous phase transition at zero temperature, where, the spins order
spontaneously. For weak coupling of the central spin to these baths, we find
that as one approaches the transition temperature, critical fluctuations make
the central spin decohere faster. Furthermore, the decoherence is maximal at
zero temperature as signalled by the divergence of the Markovian decoherence
rate.
