• Corpus ID: 3180920

On phase transition in the hard-core model on ${\bf Z}^d$

  title={On phase transition in the hard-core model on \$\{\bf Z\}^d\$},
  author={David J. Galvin and Jeff Kahn},
  journal={arXiv: Combinatorics},
It is shown that the hard-core model on ${\bf Z}^d$ exhibits a phase transition at activities above some function $\lambda(d)$ which tends to zero as $d\rightarrow \infty$ 
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We prove the existence of long-range order for the 3-state Potts antiferromagnet at low temperature on $\mathbb{Z}^d$ for sufficiently large $d$. In particular, we show the existence of six extremal
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  • 2001
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We give two examples of nonmonotonic behavior in symmetric systems exhibiting more than one critical point at which spontanoous symmetry breaking appears or disappears. The two systems are the
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For n-regular, N-vertex bipartite graphs with bipartition A U B, a precise bound is given for the sum over independent sets I of the quantity μ |I ∩ A| λ |I ∩ B| , (In other language, this is
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572 NOTICES OF THE AMS VOLUME 53, NUMBER 5 Percolation is a simple probabilistic model which exhibits a phase transition (as we explain below). The simplest version takes place on Z2, which we view
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