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We study the critical O(3) model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of conformal field theory data from correlators involving the leading O(3) singlet s, vector phi, and rank-2 symmetric tensor t. We determine their scaling dimensions to be (Delta(phi), Delta(s), Delta(t)) = (0.518942(51), 1.59489(59), 1.20954(23)), and also bound various operator product expansion coefficients. We additionally introduce a new "tip-finding" algorithm to compute an upper bound on the leading rank-4 symmetric tensor t(4), which we find to be relevant with Delta(t4) < 2.99056. The conformal bootstrap thus provides a numerical proof that systems described by the critical O(3) model, such as classical Heisenberg ferromagnets at the Curie transition, are unstable to cubic anisotropy.
Riccardo Rattazzi, Alexander Monin, Gil Badel
Riccardo Rattazzi, Alexander Monin, Eren Clément Firat, Matthew Thomas Walters