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

Ron Peled, Wojciech Samotij (2014)

Annales de l'I.H.P. Probabilités et statistiques

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 $C d^{- 1 / 3} {(log d)}^{2}$ , the model exhibits multiple hard-core measures, thus improving the previous bound of $C d^{- 1 / 4} {(log d)}^{3 / 4}$ 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...

Displaying 1 – 7 of 7

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

On constrained annealed bounds for pinning and wetting models.

On recurrent and transient sets of inhomogeneous symmetric random walks.

On the approach to equilibrium for a polymer with adsorption and repulsion.

On the dimer problem and the Ising problem in finite 3-dimensional lattices.

On the Gaussian random matrix ensembles with additional symmetry conditions.

On the occupation measure of super-Brownian motion.

Currently displaying 1 – 7 of 7

Displaying 1 – 7 of 7

Odd cutsets and the hard-core model on ℤ d

On constrained annealed bounds for pinning and wetting models.

On recurrent and transient sets of inhomogeneous symmetric random walks.

On the approach to equilibrium for a polymer with adsorption and repulsion.

On the dimer problem and the Ising problem in finite 3-dimensional lattices.

On the Gaussian random matrix ensembles with additional symmetry conditions.

On the occupation measure of super-Brownian motion.

Currently displaying 1 – 7 of 7

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