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 …

We use the conformal bootstrap to perform a precision study of the operator spectrum of the
critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central …

The formation of topological defects after a symmetry-breaking phase transition is an
overarching phenomenon that encodes the underlying dynamics. The Kibble–Zurek …

We propose a novel coarse-graining tensor renormalization group method based on the
higher-order singular value decomposition. This method provides an accurate but low …

A bstract We study the conformal bootstrap for 3D CFTs with O (N) global symmetry. We
obtain rigorous upper bounds on the scaling dimensions of the first O (N) singlet and …

Abstract The critical O (N) CFT in spacetime dimensions 2< d< 4 is one of the most important
examples of a conformal field theory, with the Ising CFT at N= 1, 2⩽ d< 4, as a notable …

We study the chiral Ising, the chiral XY, and the chiral Heisenberg models at four-loop order
with the perturbative renormalization group in 4-ε dimensions and compute critical …

We study the spin-1/2 Ising model and the Blume-Capel model at various values of the
parameter D on the simple cubic lattice. To this end we perform Monte Carlo simulations …

While the three-dimensional Ising model has defied analytic solution, various numerical
methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have …