Phase transition for the dilute clock model
We prove that phase transition occurs in the dilute ferromagnetic nearest-neighbour q-state clock model in ℤd, for every q ≥ 2 and d ≥ 2. This follows from the fact that the Edwards-Sokal random-cluster representation of the clock model stochastically dominates a supercritical Bernoulli bond percola...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03044149_v125_n10_p3879_Armendariz |
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todo:paper_03044149_v125_n10_p3879_Armendariz2023-10-03T15:20:39Z Phase transition for the dilute clock model Armendáriz, I. Ferrari, P.A. Soprano-Loto, N. Dilute clock model Phase transition Clocks Percolation (solid state) Phase transitions Solvents Bernoulli Bond percolation Clock model Low temperatures Nearest neighbour Q state Random-cluster representations Supercritical Potts model We prove that phase transition occurs in the dilute ferromagnetic nearest-neighbour q-state clock model in ℤd, for every q ≥ 2 and d ≥ 2. This follows from the fact that the Edwards-Sokal random-cluster representation of the clock model stochastically dominates a supercritical Bernoulli bond percolation probability, a technique that has been applied to show phase transition for the low-temperature Potts model. The domination involves a combinatorial lemma which is one of the main points of this article. © 2015 Elsevier B.V. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03044149_v125_n10_p3879_Armendariz |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Dilute clock model Phase transition Clocks Percolation (solid state) Phase transitions Solvents Bernoulli Bond percolation Clock model Low temperatures Nearest neighbour Q state Random-cluster representations Supercritical Potts model |
| spellingShingle |
Dilute clock model Phase transition Clocks Percolation (solid state) Phase transitions Solvents Bernoulli Bond percolation Clock model Low temperatures Nearest neighbour Q state Random-cluster representations Supercritical Potts model Armendáriz, I. Ferrari, P.A. Soprano-Loto, N. Phase transition for the dilute clock model |
| topic_facet |
Dilute clock model Phase transition Clocks Percolation (solid state) Phase transitions Solvents Bernoulli Bond percolation Clock model Low temperatures Nearest neighbour Q state Random-cluster representations Supercritical Potts model |
| description |
We prove that phase transition occurs in the dilute ferromagnetic nearest-neighbour q-state clock model in ℤd, for every q ≥ 2 and d ≥ 2. This follows from the fact that the Edwards-Sokal random-cluster representation of the clock model stochastically dominates a supercritical Bernoulli bond percolation probability, a technique that has been applied to show phase transition for the low-temperature Potts model. The domination involves a combinatorial lemma which is one of the main points of this article. © 2015 Elsevier B.V. All rights reserved. |
| format |
JOUR |
| author |
Armendáriz, I. Ferrari, P.A. Soprano-Loto, N. |
| author_facet |
Armendáriz, I. Ferrari, P.A. Soprano-Loto, N. |
| author_sort |
Armendáriz, I. |
| title |
Phase transition for the dilute clock model |
| title_short |
Phase transition for the dilute clock model |
| title_full |
Phase transition for the dilute clock model |
| title_fullStr |
Phase transition for the dilute clock model |
| title_full_unstemmed |
Phase transition for the dilute clock model |
| title_sort |
phase transition for the dilute clock model |
| url |
http://hdl.handle.net/20.500.12110/paper_03044149_v125_n10_p3879_Armendariz |
| work_keys_str_mv |
AT armendarizi phasetransitionforthediluteclockmodel AT ferraripa phasetransitionforthediluteclockmodel AT sopranoloton phasetransitionforthediluteclockmodel |
| _version_ |
1807319237588418560 |