Generalizing the Tomboulis-Yaffe Inequality to SU(N) Lattice Gauge Theories and General Classical Spin Systems

Details Generalizing the Tomboulis-Yaffe Inequality to SU(N) Lattice Gauge Theories and General Classical Spin Systems Generalizing the Tomboulis-Yaffe Inequality to SU(N) Lattice Gauge Theories and General Classical Spin Systems

2008-08-26

arxiv.org/abs/0808.3442v3

Annals of Physics 324 (2009) 1634-1665

Physics

Mathematical Physics

37 pages, 17 figures. v2: comment on an earlier work included after conclusion, figure 2 corrected. v3: the latter half revise

Scientific paper

10.1016/j.aop.2009.04.002

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.

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