Heisenberg antiferromagnet on the pyrochlore lattice

The Heisenberg antiferromagnet on the network of corner-sharing tetrahedra (the ``pyrochlore lattice'') is arguably the world's most frustrated system: the classical version of this magnet has a ground state with an extensive entropy and shows no sign of magnetic order in numerical simulations [1]. A real-life incarnation of this model is found in ZnCr$_2$O$_4$, which exhibits several peculiar effects traceable to the strong frustration: a spin-Peierls-like phase transition [2], a strongly correlated paramagnetic state with zero modes [3], and a magnetization plateau in high magnetic fields [4]. I will review recent theoretical and experimental developments in this area of research. \newline \newline [1] R. Moessner and J. T. Chalker, Phys. Rev. B {\bf 58,} 12049 (1998).\newline [2] S.-H. Lee {\em et al.}, Phys. Rev. Lett. {\bf 84,} 3718 (2000).\newline [3] S.-H. Lee {\em et al.}, Nature {\bf 418,} 856 (2002); cond-mat/0208587. [4] K. Penc, N. Shannon, and H. Shiba, Phys. Rev. Lett. {\bf 93,} 197203 (2004).