The renormalization group plays an essential role in many areas of physics, both
conceptually and as a practical tool to determine the long-distance low-energy properties of …

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 …

We review the solutions of O (N) and U (N) quantum field theories in the large N limit and as
1/N expansions, in the case of vector representations. Since invariant composite fields have …

This article is devoted to the study of the critical properties of classical XY and Heisenberg
frustrated magnets in three dimensions. We first analyze the experimental and numerical …

We describe the phase diagram of a 2+ 1-dimensional SU (2) gauge theory of fluctuating
incommensurate spin density waves for the hole-doped cuprates. Our primary assumption is …

A bstract Fixed points for scalar theories in 4− ε, 6− ε and 3− ε dimensions are discussed. It is
shown how a large range of known fixed points for the four dimensional case can be …

We consider multicomponent Abelian Higgs (AH) gauge theories with multiparameter scalar
quartic potentials, which are extensions of the SU (N)-invariant AH theories, with a smaller …

Motivated by applications to critical phenomena and open theoretical questions, we study
conformal field theories with $ O (m)\times O (n) $ global symmetry in $ d= 3$ spacetime …

We investigate the nature of the finite-temperature transition in QCD with N f massless
flavors. Universality arguments show that a continuous phase transition may exist only if …

O (n)× O (m) symmetric Landau-Ginzburg models in d= 3 dimensions possess a rich
structure of the renormalization group, which offers a theoretical prediction of the phase …