Odd cutsets and the hard-core model on Z^d

Details Odd cutsets and the hard-core model on Z^d Odd cutsets and the hard-core model on Z^d

2011-06-17

arxiv.org/abs/1106.3594v1

Mathematics

Probability

24 pages, 3 figures

Scientific paper

We consider the hard-core lattice gas model on Z^d and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds Cd^{-1/3}(log d)^2, the model exhibits multiple hard-core measures, thus improving the previous bound of Cd^{-1/4}(log d)^{3/4} given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in Z^d, the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial analysis of the structure of these cutsets yielding a quantitative form of concentration for their possible shapes as the dimension d tends to infinity. This analysis relies upon and improves previous results obtained by the first author.

Affiliated with

Also associated with

No associations

Rating

Odd cutsets and the hard-core model on Z^d does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Odd cutsets and the hard-core model on Z^d, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Odd cutsets and the hard-core model on Z^d will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-465317