0 O ct 1 99 9 Intersecting Loop Models on Z d : Rigorous Results

Abstract

We consider a general class of (intersecting) loop models in d dimensions, including those related to high-temperature expansions of well-known spin models. We find that the loop models exhibit some interesting features – often in the “unphysical” region of parameter space where all connection with the original spin Hamiltonian is apparently lost. For a particular n = 2, d = 2 model, we establish the existence of a phase transition, possibly associated with divergent loops. However, for n ≫ 1 and arbitrary d there is no phase transition marked by the appearance of large loops. Furthermore, at least for d = 2 (and n large) we find a phase transition characterised by broken translational symmetry.

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Cite this paper

@inproceedings{Chayes20080OC, title={0 O ct 1 99 9 Intersecting Loop Models on Z d : Rigorous Results}, author={Lincoln Chayes and Leonid P. Pryadko and Kirill Shtengel}, year={2008} }