L. Chayes, Leonid P. Pryadko and Kirill Shtengel
Intersecting Loop Models on Z^d : Rigorous Results
(1297K, PS, pdf)

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.