Precision Islands in the Ising and $O(N)$ Models

2016 
We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coecients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coecients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coecients obtained for the 3d Ising model, ( ; ; ; ) = (0:5181489(10); 1:412625(10); 1:0518537(41); 1:532435(19)), give the most precise determinations of these quantities to date.
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