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Explore advanced numerical methods for studying critical phenomena at boundaries and defects through Monte Carlo simulations in this comprehensive lecture. Delve into recent theoretical advances in conformal field theory and condensed matter physics that have enhanced understanding of critical systems with boundaries. Examine the boundary critical behavior of the three-dimensional O(N) model and investigate the physics underlying the recently discovered extraordinary-log phase. Analyze a class of dimerized quantum spin models whose critical behavior at edges remains incompletely understood, exploring the computational challenges and theoretical implications. Study detailed Monte Carlo calculations of the boundary operator product expansion for the three-dimensional Ising universality class across all known surface universality classes. Gain insights into how numerical simulations complement theoretical developments in understanding phase transitions and critical phenomena in systems with geometric constraints, boundaries, and defects.
