10.4225/03/58b8c5217bd05 Zhou, Zongzheng Zongzheng Zhou Phase transitions of some discrete models in statistical mechanics Monash University 2017 Phase transitions Percolation thesis(doctorate) Directed percolation ethesis-20160503-094042 Open access Face-cubic model 2016 monash:170764 1959.1/1264158 2017-03-03 01:21:35 Thesis https://bridges.monash.edu/articles/thesis/Phase_transitions_of_some_discrete_models_in_statistical_mechanics/4719778 We studied in this thesis the critical behaviours of percolation and directed percolation models using Monte Carlo simulations, including estimating percolation thresholds, critical exponents, and various universal amplitudes. In addition, we examined the geometric structure of percolation clusters, and verified the critical behaviours of a leaf-excluded percolation model belong to the standard percolation universality class. Finally, we rigorously studied an n-component face-cubic model on the complete graph, by a large deviations analysis. We proved limit theorems for the standard face-cubic model, and studied phase diagrams for the general face-cubic model.