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 prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models
with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A …

The lattice φ 4 theory in four space-time dimensions is most likely “trivial”, ie its continuum
limit is a free field theory. However, for small but positive lattice spacing a at energies well …

This paper provides a review of the literature on rigorous definitions and constructions in
quantum field theory (QFT), spanning the period of seven decades. Compared with the …

We give a direct construction of invariant measures and global flows for the stochastic
quantization equation to the quantum field theoretical $\Phi^ 4_3 $-model on the $3 …

We take the occasion of this article to review 100 years of the physical and mathematical
study of the Ising model. The model, introduced by Lenz in 1920, has been at the …

This is a primer on a mathematically rigorous renormalisation group theory, presenting
mathematical techniques fundamental to renormalisation group analysis such as Gaussian …

We study in the present article the Kardar–Parisi–Zhang (KPZ) equation ∂ _t h (t, x)= ν Δ h
(t, x)+ λ| ∇ h (t, x)|^ 2+ D\, η (t, x),\qquad (t, x) ∈ R _+ * R^ d∂ th (t, x)= ν Δ h (t, x)+ λ|∇ h (t …

We analyse and clarify the finite-size scaling of the weakly-coupled hierarchical $ n $-
component $|\varphi|^ 4$ model for all integers $ n\ge 1$ in all dimensions $ d\ge 4$, for …

We analyze in full mathematical rigor the most general quartically perturbed invariant
probability measure for a random tensor. Using a version of the Loop Vertex Expansion …