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Application of transfer matrix method to causal triangulations models

Grant number: 13/06179-2
Support Opportunities:Scholarships in Brazil - Doctorate (Direct)
Effective date (Start): July 01, 2013
Effective date (End): August 31, 2014
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Probability
Principal Investigator:Anatoli Iambartsev
Grantee:José Javier Cerda Hernández
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil


The project is focused to the study of classical spins models coupled to causal dynamical triangulation or Lorentzian triangulation. First, we consider simple models, such as the Ising model, coupled to triangulations. After that, we will study natural generalizations of it, such as the Potts model and Heisenberg model, coupled to triangulation. The method used to study of these models is the transfer matrix method and Krein-Rutman theory. This approach allows us to find regions in the quadrant of parameters (inverse temperature and fugacity), where the free energy converge and Gibbs measure of the system can be represented by a Markov chain. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
CERDA-HERNANDEZ, J.. Critical region for an Ising model coupled to causal triangulations. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, . (13/06179-2, 14/18810-1)
CERDA HERNANDEZ, J.. Potts model coupled to random causal triangulations. Journal of Mathematical Physics, v. 58, n. 12, . (14/18810-1, 13/06179-2, 12/04372-7)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
HERNÁNDEZ, José Javier Cerda. Ising and Potts model coupled to Lorentzian triangulations. 2014. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.

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