Equilibrium crystal shape of the Potts model at the first-order transition point

1997 ◽  
Vol 30 (11) ◽  
pp. 3779-3793 ◽  
Author(s):  
Masafumi Fujimoto
Keyword(s):  
Potts Model ◽  
Transition Point ◽  
Order Transition ◽  
Crystal Shape ◽  
First Order ◽  
Equilibrium Crystal Shape ◽  
First Order Transition

scholarly journals POTTS MODEL WITH INVISIBLE COLORS: RANDOM-CLUSTER REPRESENTATION AND PIROGOV–SINAI ANALYSIS

2012 ◽  
Vol 24 (02) ◽  
pp. 1250004 ◽  
Author(s):  
AERNOUT C. D. VAN ENTER ◽  
GIULIO IACOBELLI ◽  
SIAMAK TAATI
Keyword(s):  
Low Temperature ◽  
Symmetry Breaking ◽  
Potts Model ◽  
Temperature Regime ◽  
Order Transition ◽  
Ferromagnetic Interaction ◽  
Random Cluster ◽  
First Order ◽  
First Order Transition ◽  
Cluster Representation

We study a variant of the ferromagnetic Potts model, recently introduced by Tamura, Tanaka and Kawashima, consisting of a ferromagnetic interaction among q "visible" colors along with the presence of r non-interacting "invisible" colors. We introduce a random-cluster representation for the model, for which we prove the existence of a first-order transition for any q > 0, as long as r is large enough. When q > 1, the low-temperature regime displays a q-fold symmetry breaking. The proof involves a Pirogov–Sinai analysis applied to this random-cluster representation of the model.

Sign in / Sign up

Export Citation Format

Share Document