Disagreement percolation for the hard-sphere model

Abstract

Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model and the Boolean model. Non-percolation of the Boolean model implies the uniqueness of the Gibbs measure and exponential decay of pair correlations and finite volume errors. Hence, lower bounds on the critical intensity for percolation of the Boolean model imply lower bounds on the critical activity for a (potential) phase transition. These lower bounds improve upon known bounds obtained by cluster expansion techniques. The proof uses a novel dependent thinning from a Poisson point process to the hard-sphere model, with the thinning probability related to a derivative of the free energy.

References in corpus (4)

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• Effect of Dimensionality on the Continuum Percolation of Overlapping Hyperspheres and Hypercubes: II. Simulation Results and Analyses
• Cluster and virial expansions for the multi-species Tonks gas
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Cited by in corpus (6)

• On the hard sphere model and sphere packings in high dimensions
• Cluster expansions for Gibbs point processes
• On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential
• Potential-weighted connective constants and uniqueness of Gibbs measures
• Long-range orientational order of a random near lattice hard sphere and hard disk process
• Disagreement percolation for Gibbs ball models