Absence of zeros implies strong spatial mixing
arXiv:2111.04809 · doi:10.1007/s00440-023-01190-z
Abstract
In this paper we show that absence of complex zeros of the partition function of the hard-core model on any family of bounded degree graphs implies that the associated probability measure, the \emph{hard-core measure}, satisfies strong spatial mixing on that family. As a corollary we obtain that the hard-core measure on the family of bounded degree claw-free graphs satisfies strong spatial mixing. We furthermore derive strong spatial mixing for graph homomorphism measures from absence of zeros of the graph homomorphism partition function.
arXiv commentv4 some small changes based on comments by referees
References in corpus (11)
- The repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma
- Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials
- Bounds on the Complex Zeros of (Di)Chromatic Polynomials and Potts-Model Partition Functions
- Algorithmic Pirogov-Sinai theory
- Fisher zeros and correlation decay in the Ising model
- Inapproximability of the independent set polynomial in the complex plane
- Central limit theorems and the geometry of polynomials
- A Simple FPTAS for Counting Edge Covers
- Contraction: a Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems
- Correlation decay and partition function zeros: Algorithms and phase transitions
- Improved Strong Spatial Mixing for Colorings on Trees