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Disagreement percolation for the hard-sphere model. (English) Zbl 1426.82015

Summary: 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.

MSC:

82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
60E15 Inequalities; stochastic orderings
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
82B43 Percolation
60D05 Geometric probability and stochastic geometry
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Full Text: DOI arXiv Euclid

References:

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