Lattice gauge theory and a random-medium Ising model

Abstract

We study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.

10 pages, 2 figures

References in corpus (2)

• The symmetry and simplicity of the laws of physics and the Higgs boson
• Percolation and $O(1)$ loop model