Abstract Brout–Englert–Higgs physics is one of the most central and successful parts of the
standard model. It is also part of a multitude of beyond-the-standard-model scenarios. The …

This book lays the foundations of the theory of fluctuating multivalued fields with numerous
applications. Most prominent among these are phenomena dominated by the statistical …

We study the topological phase transitions occurring in three-dimensional (3D)
multicomponent lattice Abelian Higgs (LAH) models, in which an N-component scalar field is …

We study the critical behavior of three-dimensional (3D) lattice Abelian Higgs (AH) gauge
models with noncompact gauge variables and multicomponent complex scalar fields, along …

We consider multicomponent Abelian Higgs (AH) gauge theories with multiparameter scalar
quartic potentials, which are extensions of the SU (N)-invariant AH theories, with a smaller …

We investigate the nature of the deconfinement transitions in three-dimensional lattice
Abelian Higgs models, in which a complex scalar field of integer charge Q≥ 2 is minimally …

We give a review (and some improvements) of the rigorous results on the phase structure of
Abelian lattice Higgs models with gauge groups U (1) and ℝ. Emphasis is put on the relation …

We study the O (N)* transitions that occur in the 3D Z 2-gauge N-vector model and the
analogous Ising* transitions occurring in the 3D Z 2-gauge Higgs model, corresponding to …

In this paper, we prove that Bernoulli percolation on bounded degree graphs with
isoperimetric dimension d> 4 undergoes a nontrivial phase transition (in the sense that pc< …

Quantization of solitons in terms of Euclidean region functional integrals is developed, and
Osterwalder-Schrader reconstruction is extended to theories with topological solitons. The …