Generalizing the Tomboulis–Yaffe inequality to [formula omitted] lattice gauge theories and general classical spin systems

Abstract

We extend the inequality of Tomboulis and Yaffe in SU ( 2 ) lattice gauge theory (LGT) to SU ( N ) LGT and to general classical spin systems, by use of reflection positivity. Basically the inequalities guarantee that a system in a box that is sufficiently insensitive to boundary conditions has a non-zero mass gap. We explicitly illustrate the theorem in some solvable models. Strong-coupling expansion is then utilized to discuss some aspects of the theorem. Finally, a conjecture for exact expression to the off-axis mass gap of the triangular Ising model is presented. The validity of the conjecture is tested in multiple ways.