This book presents analytic and numerical studies of
magnetism in strongly correlated solid-state systems.
Competing tendencies in these systems can lead to
spontaneous nanoscale structures, such as stripes and
checkerboards. There are three topics explored in
this book. First, spin waves and magnetic excitations
for well-ordered spin structures are studied by using
a suitably parametrized Heisenberg
model. Both site-centered and bond-centered antiphase
domain walls are considered for a range of spacings
between stripes and checkerboard antiphase domain
walls. Second, quasi-two-dimensional spin systems are
explored by using the Stochastic Series Expansion
Quantum Monte Carlo method. The order-disorder phase
transitions are studied for both static and dynamic
bond-diluted Heisenberg spin systems. Varying the
interlayer coupling, the Neel temperature and
universal scalings are studied for weakly coupled
Heisenberg antiferromagnetic layers consisting of
coupled ladders. Third, a two-dimensional Heisenberg
antiferromagnet with nearest-neighbor and four-spin
ring exchange is studied, which exhibits a quantum
phase transition from the Valence Bond Solid phase to
Neel order.