On Phase Transition in the Hard-Core Model on ${\mathbb Z}^d$

2004 ◽  
Vol 13 (2) ◽  
pp. 137-164 ◽  
Author(s):  
DAVID GALVIN ◽  
JEFF KAHN
Keyword(s):  
Phase Transition ◽  
Hard Core ◽  
Core Model ◽  
Hard Core Model

An Entropy Approach to the Hard-Core Model on Bipartite Graphs

2001 ◽  
Vol 10 (3) ◽  
pp. 219-237 ◽  
Author(s):  
JEFF KAHN
Keyword(s):  
Phase Transition ◽  
Bipartite Graph ◽  
Upper Bound ◽  
Hard Core ◽  
Independent Set ◽  
Independent Sets ◽  
Bipartite Graphs ◽  
Core Model ◽  
Hard Core Model ◽  
Regular Bipartite Graph

We use entropy ideas to study hard-core distributions on the independent sets of a finite, regular bipartite graph, specifically distributions according to which each independent set I is chosen with probability proportional to λ[mid ]I[mid ] for some fixed λ > 0. Among the results obtained are rather precise bounds on occupation probabilities; a ‘phase transition’ statement for Hamming cubes; and an exact upper bound on the number of independent sets in an n-regular bipartite graph on a given number of vertices.

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

2015 ◽  
Vol 29 (4) ◽  
pp. 1895-1915 ◽  
Author(s):  
Juan C. Vera ◽  
Eric Vigoda ◽  
Linji Yang
Keyword(s):  
Phase Transition ◽  
Hard Core ◽  
Core Model ◽  
Hard Core Model

scholarly journals Percolation games, probabilistic cellular automata, and the hard-core model

2018 ◽  
Vol 174 (3-4) ◽  
pp. 1187-1217 ◽  
Author(s):  
Alexander E. Holroyd ◽  
Irène Marcovici ◽  
James B. Martin
Keyword(s):  
Cellular Automata ◽  
Hard Core ◽  
Core Model ◽  
Probabilistic Cellular Automata ◽  
Hard Core Model

``Hard‐Core'' Model of Liquids

1966 ◽  
Vol 45 (1) ◽  
pp. 378-383 ◽  
Author(s):  
Neil S. Snider
Keyword(s):  
Hard Core ◽  
Core Model ◽  
Hard Core Model

scholarly journals Liquid-solid transitions in the three-body hard-core model

2015 ◽  
Vol 109 (2) ◽  
pp. 20003
Author(s):  
Tommaso Comparin ◽  
Sebastian C. Kapfer ◽  
Werner Krauth
Keyword(s):  
Hard Core ◽  
Core Model ◽  
Three Body ◽  
Hard Core Model

Phase Transitions in 2:1 and 3:1 Hard-Core Model Electrolytes

2002 ◽  
Vol 88 (4) ◽  
Author(s):  
Athanassios Z. Panagiotopoulos ◽  
Michael E. Fisher
Keyword(s):  
Phase Transitions ◽  
Hard Core ◽  
Core Model ◽  
Hard Core Model

scholarly journals The Widom–Rowlinson model, the hard-core model and the extremality of the complete graph

2017 ◽  
Vol 62 ◽  
pp. 70-76 ◽  
Author(s):  
Emma Cohen ◽  
Péter Csikvári ◽  
Will Perkins ◽  
Prasad Tetali
Keyword(s):  
Complete Graph ◽  
Hard Core ◽  
Core Model ◽  
Hard Core Model
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