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

We prove that a convex phase may be perturbed into a non-convex phase prese rving the spectral gap properties of the unbounded spin system with nearest neighbour interaction associated to this potential. The proof is based on Heifer's method hat reduces the spectral properties of the unbounded spin s ystem to some uniform spectral gap of the one-dimensional phase. We then ma ke: use of Hardy's criterion for Poincare inequalities on the real line to construct our examples. (C) 2001 Academic Press.