Properties of a Classical Spin Liquid: The Heisenberg Pyrochlore Antiferromagnet

We study the low-temperature behavior of the classical Heisenberg antiferromagnet with nearest neighbor interactions on the pyrochlore lattice. Because of geometrical frustration, the ground state of this model has an extensive number of degrees of freedom. We show, by analyzing the effects of small fluctuations around the ground-state manifold, and from the results of Monte Carlo and molecular dynamics simulations, that the system is disordered at all temperatures T and has a finite relaxation time, which varies as $T^{-1\mathrm{}}$ for small T.