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.
Cite
@article{arxiv.cond-mat/9910292,
title = {Intersecting Loop Models on Z^D: Rigorous Results},
author = {L. Chayes and Leonid P. Pryadko and Kirill Shtengel},
journal= {arXiv preprint arXiv:cond-mat/9910292},
year = {2007}
}
Comments
LaTeX+elsart.cls; 30 p., 6 figs; submitted to Nucl. Phys. B; a few minor typos corrected