POTTS MODEL WITH INVISIBLE COLORS: RANDOM-CLUSTER REPRESENTATION AND PIROGOV–SINAI ANALYSIS
2012 ◽
Vol 24
(02)
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pp. 1250004
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Keyword(s):
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.
2000 ◽
Vol 12
(10)
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pp. 2233-2243
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Keyword(s):
1997 ◽
Vol 30
(11)
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pp. 3779-3793
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Keyword(s):
1983 ◽
Vol 16
(15)
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pp. 2833-2845
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Reply to Comment on Equilibrium crystal shape of the Potts model at the first-order transition point
2002 ◽
Vol 35
(34)
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pp. 7553-7557
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Keyword(s):
1993 ◽
Vol 23
(8)
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pp. 547-552
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Keyword(s):
1993 ◽
Vol 26
(13)
◽
pp. 3045-3062
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Keyword(s):
1990 ◽
Vol 59
(4)
◽
pp. 1293-1298
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Keyword(s):
Keyword(s):
2002 ◽
Vol 35
(34)
◽
pp. 7549-7552
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Keyword(s):