Percolation and phase transitions: Numerical studies

From subgraph expansions of Ising‐type models in external fields, phase transitions of Ising‐type models have been related to percolation transitions of corresponding correlated percolation models. From Monte Carlo simulations of hard‐core particles on lattices, phase transitions of such systems have been related to percolation transitions of site‐correlated percolation problems. In this talk, we review recent numerical studies of lattice interacting systems based on such connections. The topics under discussion include percolation renormalization group approach to lattice systems, cluster Monte Carlo studies of the Potts model on hypercubic lattices, Monte Carlo calculations of the free energy and geometrical factors for the Potts model, etc.