Phase transitions are one of the most fascinating, and also most perplexing, phenomena in
equilibrium statistical mechanics. On the physics side, many approximate methods to …

We prove that various SO (n)-invariant n-vector models with interactions which have a deep
and narrow enough minimum have a first-order transition in the temperature. The result …

Graphical representations similar to the FK representation are developed for a variety of spin-
systems. In several cases, it is established that these representations have (FKG) …

In this outline of a program, based on rigorous renormalization group theory, we introduce
new definitions which allow one to formulate precise mathematical conjectures related to …

Quantum statistical mechanics plays a major role in many fields such as thermodynamics,
plasma physics, solid-state physics, and the study of stellar structure. While the theory of …

We establish a surface order large deviation estimate for the magnetisation of low
temperature ϕ 3 4. As a byproduct, we obtain a decay of spectral gap for its Glauber …

We consider various sufficiently nonlinear vector models of ferromagnets, of nematic liquid
crystals and of nonlinear lattice gauge theories with continuous symmetries. We show …

We study the well-known sociological phenomenon of gang aggregation and territory
formation through an interacting agent system defined on a lattice. We introduce a two-gang …

We study the classical version of the 120∘-model. This is an attractive nearest-neighbor
system in three dimensions with XY (rotor) spins and interaction such that only a particular …

We consider a general class of (intersecting) loop models in d dimensions, including those
related to high-temperature expansions of well-known spin models. We find that the loop …