Explore critical phenomena in φ4 and Blume-Capel models through this comprehensive colloquium lecture. Delve into the generalization of the Ising model of ferromagnetism, examining the origins of these lattice spin models in lattice quantum field theory and statistical physics of uranium dioxide. Investigate the phase transitions in these models and the limited rigorous results concerning their critical phases. Learn about the recent progress in the mathematical study of critical phenomena in the Ising model and the crucial role of percolation theory in understanding connectivity properties of random graphs. Discover how percolation techniques can be extended to analyze critical phenomena in the φ4 and Blume-Capel models, despite their lack of symmetries and integrability compared to the Ising model. Gain insights from speaker Trishen Gunaratnam of the University of Geneva, Switzerland, as he presents this fascinating exploration of advanced concepts in statistical physics and quantum field theory. Read more