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Explore advanced numerical methods for studying phase transitions in statistical and quantum lattice models through this 59-minute conference talk. Delve into the application of Conformal Perturbation Theory (CPT) and fuzzy sphere regulators for analyzing 3D Ising and O(2) models with exact rotational invariance. Learn how to systematically compare finite-volume numerical results to infinite-volume Conformal Field Theory (CFT) data by utilizing the sphere S^(d-1) as the spatial manifold. Discover a comprehensive framework for determining critical points, speed of light calculations, and understanding residual deviations from CFT predictions. Master techniques for extracting Operator Product Expansion (OPE) coefficients from fuzzy sphere data through novel methods that leverage energy level sensitivity to detuning from criticality. Examine finite-size corrections, level mixing phenomena, and avoided crossings in finite systems while gaining insights into minimizing systematic effects through proper model tuning. The presentation includes validation studies of CPT applications in 1+1D Ising models away from integrable limits, providing both theoretical foundations and practical computational approaches for advanced condensed matter physics research.
