Generalizing the Tomboulis–Yaffe inequality to image lattice gauge theories and general classical spin systems Original Research Article

We extend the inequality of Tomboulis and Yaffe in image lattice gauge theory (LGT) to image 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.