99-415 L. Chayes, Leonid P. Pryadko and Kirill Shtengel

Intersecting Loop Models on Z^d : Rigorous Results (1297K, PS, pdf) Nov 1, 99

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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.

Files: 99-415.src( 99-415.keywords , loops.pdf.mm , loops.ps.gz.mm )