We review results concerning the critical behavior of spin systems at equilibrium. We
consider the Ising and the general O (N)-symmetric universality classes, including the N→ 0 …

The successes and limitations of statistical sampling for a sequence of models studied in the
context of lattice QCD are discussed and the need for new methods to deal with finite …

NATURE abounds with phase transitions. The boiling and freezing of water are everyday
examples of phase transitions, as are more exotic processes such as superconductivity and …

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

We construct lattice gauge theories in which the elements of the link matrices are
represented by non-commuting operators acting in a Hilbert space. These quantum link …

We propose to compute the running coupling g 2 in lattice gauge theories and non-linear σ-
models through a finite-size scaling analysis. The idea is shown to work well in the O (3) σ …

Known Bethe ansatz results about the sine–Gordon factorized scattering are reinterpreted in
terms of perturbed conformal field theory. We obtain an exact relation between the ultraviolet …

We consider high spin operators. We give a general argument for the logarithmic scaling of
their anomalous dimensions which is based on the symmetries of the problem. By an …

There exist lattice actions which give cut-off independent physical predictions even on
coarse grained lattices. Rotation symmetry is restored, the spectrum becomes exact and, in …

In this review recent developments in chiral perturbation theory (CHPT), which is the
effective field theory of the standard model below the chiral symmetry breaking scale, are …