Disagreement percolation for the hard-sphere model

2015/07/09 by Christoph Hofer-Temmel, Hofer-Temmel, Christoph · 1 citation
Mathematics · Physics and Astronomy · #82B21 (60E15 60K35 60G55 82B43 60D05) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1507.02521

openalex publication_date 2015/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Long-range orientational order of a random near lattice hard sphere and hard disk process

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