Application of transfer matrix method to causal triangulations models

Abstract

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)