The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge theory

TL;DR

This paper investigates the vacuum structure of three-dimensional SU(2) lattice gauge theory under an external magnetic field, providing evidence for a nontrivial minimum supporting a ferromagnetic gluon condensate.

Contribution

It presents the first lattice simulation evidence of a nontrivial vacuum minimum, supporting Savvidy's ferromagnetic gluon condensation hypothesis in three dimensions.

Findings

Evidence of a nontrivial minimum in the effective potential.

Supports the ferromagnetic gluon condensation picture.

Analyzes scaling and finite volume effects systematically.

Abstract

The vacuum effective potential of three-dimensional SU(2) lattice gauge theory in an applied color-magnetic field is computed over a wide range of field strengths. The background field is induced by an external current, as in continuum field theory. Scaling and finite volume effects are analyzed systematically. The first evidence from lattice simulations is obtained of the existence of a nontrivial minimum in the effective potential. This supports a ``ferromagnetic'' picture of gluon condensation, proposed by Savvidy on the basis of a one-loop calculation in (3+1)-dimensional QCD.