Journal reference: Annals of Applied Probability 2008, Vol. 18, No. 5, 1897-1909
Comments: Published in at http://dx.doi.org/10.1214/07-AAP508 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Counter to the general notion that the regular tree is the worst case for decay of correlation between sets and nodes, we produce an example of a multi-spin interacting system which has uniqueness on the d-regular tree but does not have uniqueness on some infinite d-regular graphs.
@article{arxiv.0704.2916,
title = {Uniqueness thresholds on trees versus graphs},
author = {Allan Sly},
journal= {arXiv preprint arXiv:0704.2916},
year = {2008}
}