Abstract

We consider the lattice Higgs model on ${\mathbb{Z}}^4$ in the fixed length limit, with structure group given by ${\mathbb{Z}}_n$ for $n\ge 2$. We compute the expected value of the Wilson loop observable to leading order when the inverse temperature and hopping parameter are both sufficiently large compared to the length of the loop. The leading order term is expressed in terms of a quantity arising from the related but much simpler ${\mathbb{Z}}_n$ model, which reduces to the usual Ising model when $n=2$. As part of the proof, we construct a coupling between the lattice Higgs model and the ${\mathbb{Z}}_n$ model.

Keywords

Mathematical Subject Classification

Milestones

Authors