Percolation and phase transition of spin systems on Lorentzian random graphs

• Grant number: 14/18810-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2014
• End date: August 29, 2016
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Serguei Popov
• Grantee: José Javier Cerda Hernández
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 15/16407-8 - Phase transition and critical phenomena in two-dimensional discrete quantum gravity, BE.EP.PD

Abstract

The project is focused on the study of bond percolation on causal triangulations (CTs) or Lorentzian random graph and phase transition of spin system coupled to CTs. From a physical point of view it is interesting to study various models of gravity-matter, such as the Ising and Potts models coupled to CTs. Based in the relation between percolation and phase transition of spin systems, the project will study bond percolation on CTs in the quenched case. Unlike the classical examples, here the enviroment in which the percolation occurs is itself random, this means that the techniques needed to establish the critical probability are rather different. There exists a conjecture that the critical value equals 1/2.

Scientific publications

(4)

(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, FEB 2017. (13/06179-2, 14/18810-1)

CERDA HERNANDEZ, J.. Potts model coupled to random causal triangulations. Journal of Mathematical Physics, v. 58, n. 12, DEC 2017. (14/18810-1, 13/06179-2, 12/04372-7)

CERDA-HERNANDEZ, JOSE; YAMBARTSEV, ANATOLY; ZOHREN, STEFAN. On the critical probability of percolation on random causal triangulations. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 31, n. 2, p. 215-228, MAY 2017. (14/18810-1)

CERDA-HERNANDEZ, J.. Critical region for an Ising model coupled to causal triangulations. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, v. N/A, p. 25-pg., 2017-02-01. (13/06179-2, 14/18810-1)