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 …

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 …

A bstract In theories with renormalons the perturbative series is factorially divergent even
after restricting to a given order in 1/N, making the 1/N expansion a natural testing ground for …

A bstract We study the free energy of integrable, asymptotically free field theories in two
dimensions coupled to a conserved charge. We develop methods to obtain analytic …

We carry out a high-precision Monte Carlo simulation of the two-dimensional O (3)-invariant
σ model at correlation lengths ξ up to∼ 1 0 5. Our work employs a powerful method for …

We present some evidence that in lattice gauge theory the condensate contains a non-
perturbative contribution proportional to Λ2, the square of the physical scale. This result is …

Numerical simulations of two-dimensional CP N− 1 models are performed at N= 2, 1 0, and
21. The lattice action adopted depends explicitly on the gauge degrees of freedom and …

Abstract We analyze quantum Monte Carlo data in the vicinity of the quantum transition
between a Néel state and a quantum paramagnet in a two-layer, square-lattice spin-1/2 …

The Shifman--Vainshtein--Zakharov (SVZ) sum rules provide a method to obtain trans-series
expansions in many quantum field theories, in which exponentially small corrections are …