| Autor: |
Ananikian, N., Izmailyan, N. Sh., Johnston, D. A., Kenna, R., Ranasinghe, R. P. K. C. M. |
| Rok vydání: |
2013 |
| Předmět: |
|
| Zdroj: |
J. Phys. A: Math. Theor. 46 (2013) 385002 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1088/1751-8113/46/38/385002 |
| Popis: |
The number of so-called invisible states which need to be added to the q-state Potts model to transmute its phase transition from continuous to first order has attracted recent attention. In the q=2 case, a Bragg-Williams, mean-field approach necessitates four such invisible states while a 3-regular, random-graph formalism requires seventeen. In both of these cases, the changeover from second- to first-order behaviour induced by the invisible states is identified through the tricritical point of an equivalent Blume-Emery-Griffiths model. Here we investigate the generalised Potts model on a Bethe lattice with z neighbours. We show that, in the q=2 case, r_c(z)=[4 z / 3(z-1)] [(z-1)/(z-2)]^z invisible states are required to manifest the equivalent Blume-Emery-Griffiths tricriticality. When z=3, the 3-regular, random-graph result is recovered, while the infinite z limit delivers the Bragg-Williams, mean-field result. |
| Databáze: |
arXiv |
| Externí odkaz: |
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