Percolation and phase transition of spin systems on Lorentzian random graphs
| Full text | |
| Author(s): |
Cerda Hernandez, J.
Total Authors: 1
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| Document type: | Journal article |
| Source: | Journal of Mathematical Physics; v. 58, n. 12 DEC 2017. |
| Web of Science Citations: | 0 |
| Abstract | |
In this work, we study the annealed Potts model coupled to two-dimensional causal triangulations (CTs). Employing duality of graphs, weprove that in the thermodynamic limit, the Potts model coupled to causal triangulations with parameters beta and mu is equivalent to a Potts model coupled to dual causal triangulations at the dual parameters beta{*} = log(1 + q/(e(beta) - 1)) and mu{*} = mu - 3/2log(e(beta) - 1) + log q. This duality relation follows from the Fermi-Kurie representation for the Potts model. Employing our duality relation, we determine a region where the critical curve for the annealed model can be located. We also provide lower and upper bounds for the infinite-volume free energy. Published by AIP Publishing. (AU) | |
| FAPESP's process: | 14/18810-1 - Percolation and phase transition of spin systems on Lorentzian random graphs |
| Grantee: | José Javier Cerda Hernández |
| Support type: | Scholarships in Brazil - Post-Doctorate |
| FAPESP's process: | 13/06179-2 - Application of transfer matrix method to causal triangulations models |
| Grantee: | José Javier Cerda Hernández |
| Support type: | Scholarships in Brazil - Doctorate (Direct) |
| FAPESP's process: | 12/04372-7 - Probabilistic aspects of causal dynamical triangulations |
| Grantee: | Anatoli Iambartsev |
| Support type: | Regular Research Grants |