Application of transfer matrix method to causal triangulations models
Percolation and phase transition of spin systems on Lorentzian random graphs
Probabilistic aspects of causal dynamical triangulations: percolation
| Full text | |
| Author(s): |
Cerda-Hernandez, J.
Total Authors: 1
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| Document type: | Journal article |
| Source: | JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; v. N/A, p. 25-pg., 2017-02-01. |
| Abstract | |
This paper extends the results obtained by Hernandez et al for the annealed Ising model coupled to two-dimensional causal dynamical triangulations. We employ the Fortuin-Kasteleyn (FK) representation in order to determine a region in the quadrant of the parameters beta, mu > 0 where the critical curve for the annealed model is possibly located. This can be done by outlining a region where the model has a unique infinite-volume Gibbs measure, and a region where the finite-volume Gibbs measure does not have weak limit (in fact, does not exist if the volume is large enough). We also improve the region where the model has a one dimensional geometry with respect to the unique weak limit measure, which implies that the Ising model on causal triangulation does not have phase transition in this region. Furthermore, we provide a better approximation of the free energy for the coupled model. (AU) | |
| FAPESP's process: | 13/06179-2 - Application of transfer matrix method to causal triangulations models |
| Grantee: | José Javier Cerda Hernández |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |
| FAPESP's process: | 14/18810-1 - Percolation and phase transition of spin systems on Lorentzian random graphs |
| Grantee: | José Javier Cerda Hernández |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |