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 …

Great effort is presently being expended in the search for elementary scalar “Higgs”
particles. These particles have yet to be observed. The primary justification for this search is …

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 …

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and
prove some rigorous theorems on the regularity properties and possible pathologies of the …

Simple random walks-or equivalently, sums of independent random vari ables-have long
been a standard topic of probability theory and mathemat ical physics. In the 1950s, non …

We discuss the analytic structure of off-shell correlation functions in Little String Theories
(LSTs) using their description as asymptotically linear dilaton backgrounds of string theory …

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 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 consider the critical behaviour of long-range O (n) O (n) models (n ≥ 0 n≥ 0) on Z^ d Z
d, with interaction that decays with distance r as r^-(d+ α) r-(d+ α), for α ∈ (0, 2) α∈(0, 2). For …