scholarly journals Continuity of the Phase Transition for Planar Random-Cluster and Potts Models with $${1 \le q \le 4}$$ 1 ≤ q ≤ 4

2016 ◽  
Vol 349 (1) ◽  
pp. 47-107 ◽  
Author(s):  
Hugo Duminil-Copin ◽  
Vladas Sidoravicius ◽  
Vincent Tassion
Keyword(s):  
Phase Transition ◽  
Potts Models ◽  
Random Cluster

scholarly journals Phase transition in continuum Potts models

1996 ◽  
Vol 181 (2) ◽  
pp. 507-528 ◽  
Author(s):  
H. -O. Georgii ◽  
O. Häggström
Keyword(s):  
Phase Transition ◽  
Potts Models

scholarly journals Phase transition properties of 3D Potts models

2008 ◽  
Vol 802 (3) ◽  
pp. 421-434 ◽  
Author(s):  
Alexei Bazavov ◽  
Bernd A. Berg ◽  
Santosh Dubey
Keyword(s):  
Phase Transition ◽  
Potts Models

scholarly journals Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models

2014 ◽  
Vol 330 (3) ◽  
pp. 1339-1394 ◽  
Author(s):  
Roman Kotecký ◽  
Alan D. Sokal ◽  
Jan M. Swart
Keyword(s):  
Phase Transition ◽  
Low Temperature ◽  
Potts Models

scholarly journals Percolation results for the continuum random cluster model

2018 ◽  
Vol 50 (01) ◽  
pp. 231-244 ◽  
Author(s):  
Pierre Houdebert
Keyword(s):  
Phase Transition ◽  
Cluster Model ◽  
Boolean Model ◽  
Connected Components ◽  
Random Structure ◽  
Stochastic Domination ◽  
Random Cluster Model ◽  
Random Cluster ◽  
Fixed Parameter ◽  
The Continuum

Abstract The continuum random cluster model is a Gibbs modification of the standard Boolean model with intensity z > 0 and law of radii Q. The formal unnormalised density is given by q N cc , where q is a fixed parameter and N cc is the number of connected components in the random structure. We prove for a large class of parameters that percolation occurs for large enough z and does not occur for small enough z. We provide an application to the phase transition of the Widom–Rowlinson model with random radii. Our main tools are stochastic domination properties, a detailed study of the interaction of the model, and a Fortuin–Kasteleyn representation.

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