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 many-body physics at quantum phase transitions shows a subtle interplay between
quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we …

This book explains in detail how to perform perturbation expansions in quantum field theory
to high orders, and how to extract the critical properties of the theory from the resulting …

Recently the series for two renormalization group functions (corresponding to the
anomalous dimensions of the fields and) of the three-dimensional field theory have been …

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 improve the theoretical estimates of the critical exponents for the three-dimensional
Heisenberg universality class. We find γ= 1.3960 (9), ν= 0.7112 (5), η= 0.0375 (5), α …

We improve the theoretical estimates of the critical exponents for the three-dimensional XY
universality class. We find α=− 0.0146 (8), γ= 1.3177 (5), ν= 0.671 55 (27), η= 0.0380 (4), β …

Abstract 25th-order high-temperature series are computed for a general nearest-neighbor
three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In …

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 …

Abstract We consider the Ginzburg-Landau Hamiltonian with a cubic-symmetric quartic
interaction and compute the renormalization-group functions to six-loop order in d= 3. We …