Publisher Summary This chapter discusses percolation theory as well as spin-glass
phenomena, the former of which is used to understand subjects as diverse as fluid flow in …

Two-dimensional arrays of interacting magnetic nanostructures offer a remarkable
playground for simulating, experimentally, lattice spin models. Initially designed to capture …

We report a detailed study of the pyrochlore Ho 2 Ti 2 O 7, in which the magnetic ions (Ho
3+) are ferromagnetically coupled with J∼ 1 K. We show that the presence of local Ising …

A ferromagnet with spin anisotropies on the two-dimensional (2D) kagomé lattice is
theoretically studied. This is a typical example of the flat-band ferromagnet. The Berry phase …

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 …

We compare the behaviour of ferromagnetic and antiferromagnetic Ising-type spin models
on the cubic pyrochlore lattice. With simpleup-down'Ising spins, the antiferromagnet is highly …

Due to the particular geometry of the kagomé lattice, it is shown that antisymmetric
Dzyaloshinsky-Moriya interactions are allowed and induce magnetic ordering. The …

The newly discovered frustrated pyrochlore ferromagnet (“spin ice”) is investigated using
Monte Carlo simulations. The ground state is disordered and infinitely degenerate, but in an …

We study the classical Heisenberg model for spins on a pyrochlore lattice interacting via
long-range dipole-dipole forces and nearest-neighbor exchange. Antiferromagnetic …

The Heisenberg nearest-neighbor antiferromagnet on the pyrochlore (three-dimensional)
lattice is highly frustrated and does not order at low temperature where spin-spin …