Within the past 20 years or so, there has occurred an explosion of interest in the magnetic
behavior of pyrochlore oxides of the type A 2 3+ B 2 4+ O 7, where A is a rare-earth ion and …

We present a detailed overview of numerical Monte Carlo studies of the dipolar spin ice
model, which has been shown to be an excellent quantitative descriptor of the Ising …

Ordering of the frustrated classical Heisenberg model on the triangular lattice with an
incommensurate spiral structure is studied under magnetic fields by means of a mean-field …

The current state of efforts to understand the phenomenon of geometric magnetic frustration
is described in the context of several key materials. All are transition metal oxides which …

The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-
dimensional spin system with a rich phase diagram. Besides hosting several ordered …

We study the low-temperature behavior of the classical Heisenberg antiferromagnet with
nearest neighbor interactions on the pyrochlore lattice. Because of geometrical frustration …

Recent experiments suggest that the Ising pyrochlore magnets Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O
7 display qualitative properties of the nearest-neighbor “spin ice” model. We discuss the …

We present the general theory of clean, two-dimensional, quantum Heisenberg
antiferromagnets which are close to the zero-temperature quantum transition between …

We study the ground-state and low-energy properties of classical vector spin models with
nearest-neighbor antiferromagnetic interactions on a class of geometrically frustrated …

Neutron scattering, muon spin relaxation, and dc susceptibility studies have been carried out
on polycrystalline Tb 2 Ti 2 O 7, a pyrochlore antiferromagnet in which the Tb 3+ moments …