✦ LIBER ✦

Spectral Gaps for Spin Systems: Some Non-convex Phase Examples

✍ Scribed by Ivan Gentil; Cyril Roberto

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 164 KB
Volume: 180
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3692

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✦ Synopsis

We prove that a convex phase may be perturbed into a non-convex phase preserving the spectral gap properties of the unbounded spin system with nearest neighbour interaction associated to this potential. The proof is based on Helffer's method hat reduces the spectral properties of the unbounded spin system to some uniform spectral gap of the one-dimensional phase. We then make use of Hardy's criterion for Poincare inequalities on the real line to construct our examples.