Spectral gaps for spin systems: Some non-convex phase examples (Q5929867)

Spectral gap property is established for a class of unbounded spin systems with nearest neighbour interaction and non-convex phases. The proof is based on the Helffer method of relating spectral properties of unbounded spin systems to those of one-dimensional systems [\textit{B. Helffer}, Ann. Inst. Henri Poincaré, Probab. Stat. 35, No. 4, 483-508 (1999)] combined with the Hardy criterion for Poincaré inequalities on the real line.