# Unitary dressing transformations and exponential decay below threshold for quantum spin systems. Parts III and IV

Article

- Received:

DOI: 10.1007/BF02097702

- Cite this article as:
- Albanese, C. Commun.Math. Phys. (1990) 134: 237. doi:10.1007/BF02097702

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## Abstract

This is the continuation of a series of articles concerning a class of quantum spin systems with Hamiltonian operators of the form where Λ is a graph, λ is a small parameter and

$$H_\lambda = \sum\limits_{x \in \Lambda } {s_x + } \sum\limits_{yo \subset \Lambda } {\lambda ^{\left| {yo} \right|_c - 1} } t_{yo} $$

*s*_{x}has a gap≥1 for all x ε Λ\I In the singular setI ⊂ Λ, the gap of*s*_{x}can be arbitrarily small. Part III is devoted to the proof of a preliminary result, while in Part IV we consider the case in whichI is a subset of finite density of Λ. This completes the first iteration step of the deterministic part of the proof of localization in the ground state of the random field quantum*XY*model.## Copyright information

© Springer-Verlag 1990