Improved Bounds on the Phase Transition for the Hard-Core Model in 2-Dimensions

DOI10.1007/978-3-642-40328-6_48zbMath1405.68230arXiv1306.0431OpenAlexW2189760036MaRDI QIDQ2851895

Eric Vigoda, Linji Yang, Juan Carlos Vera

Publication date: 4 October 2013

Published in: SIAM Journal on Discrete Mathematics, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.0431

zbMATH Keywords

linear programminguniquenessphase transitionMCMCapproximate countinghard-core modelstrong spatial mixingbranching matrices

Mathematics Subject Classification ID

Linear programming (90C05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) (68Q87)

Related Items (9)

Spatial mixing and the connective constant: optimal bounds ⋮ Representation and poly-time approximation for pressure of \(\mathbb Z^2\) lattice models in the non-uniqueness region ⋮ Algorithms to approximately count and sample conforming colorings of graphs ⋮ Sampling weighted perfect matchings on the square-octagon lattice ⋮ Perfect Sampling in Infinite Spin Systems Via Strong Spatial Mixing ⋮ Analyticity for classical gasses via recursion ⋮ Convergence of MCMC and Loopy BP in the Tree Uniqueness Region for the Hard-Core Model ⋮ Phase Coexistence for the Hard-Core Model on ℤ² ⋮ Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model

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