I will summarize progress at using the conformal bootstrap to solve 3d CFTs. These include the critical 3d Ising model, the O(N) vector models, and the minimal 3d SCFT. Recent results for the O(2) model resolve a longstanding discrepancy between experiment and Monte Carlo simulations, while results for the O(3) model prove the instability of Heisenberg magnets to cubic anisotropy.
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