This article reviews, from a very personal point of view, the origins and the early work on
transitions driven by topological defects such as vortices in the two dimensional planar rotor …

Josephson-junction arrays are ideal model systems to study a variety of phenomena such as
phase transitions, frustration effects, vortex dynamics and chaos. In this review, we focus on …

Magnetism plays a key role in modern science and technology, but still many open
questions arise from the interplay of magnetic many-body interactions. Deeper insight into …

We present details of a stochastic generalization of the multigrid method, called multigrid
Monte Carlo (MGMC), that reduces critical slowing down in Monte Carlo computations of …

The Heisenberg antiferromagnet on a two-dimensional triangular lattice is a paradigmatic
problem in frustrated magnetism. Even in the classical limit S→∞, its properties are far from …

The dynamics of an ensemble of bistable elements with global time-delayed coupling under
the influence of noise is studied analytically and numerically. Depending on the noise level …

We study the quantum phase transition between the insulating and the globally coherent
superfluid phases in the Bose-Hubbard model with T 3 structure, the “dice lattice.” Even in …

Renormalization-group analysis is employed to investigate the critical behavior of coupled
XY models. Recursion relations for small vortex fugacities and Migdal recursion relations in …

We study the critical behavior of fully frustrated XY and Josephson-junction systems by
means of a coupled XY-Ising model. From Monte Carlo and transfer-matrix calculations, we …

We investigate the nature of phase transitions in a generalized uniformly frustrated square-
lattice model with XY spins. The frustration is made to vary by changing the negative bond …