We present asymptotically exact results for the real time order parameter correlations of a class of $d=1\mathrm{}$ Ising models in a transverse field at low temperatures ( $T$) on both sides of the quantum critical point. The correlations are a product of a $T$-independent factor determined by quantum effects, and a $T$-dependent relaxation function which comes from a classical theory. We confirm our predictions by a no-free-parameter comparison with numerical studies on the nearest neighbor spin-1/2 model.

• Received 19 September 1996

DOI:https://doi.org/10.1103/PhysRevLett.78.2220