Finite temperature dynamics near quantum phase transitions

We review the non-zero temperature relaxational dynamics of quantum systems near a zero temperature, second-order phase transition. We begin with the quantum Ising chain, for which universal and exact results for the relaxation rates can be obtained in all the distinct limiting regimes of the phase diagram. Next, we describe the crossovers in the electron spectral function near a transition involving a change in the pairing symmetry of BCS superconductors in two dimensions. Finally, we consider dynamic spin models which may provide a mean-field description of magnetic ordering transitions in the heavy fermion compounds.