We use the conformal bootstrap to perform a precision study of the operator
spectrum of the critical 3d Ising model. We conjecture that the 3d Ising
spectrum minimizes the central charge c in the space of unitary solutions to
crossing symmetry. Because extremal solutions to crossing symmetry are uniquely
determined, we are able to precisely reconstruct the first several Z2-even
operator dimensions and their OPE coefficients. We observe that a sharp
transition in the operator spectrum occurs at the 3d Ising dimension
Delta_sigma=0.518154(15), and find strong numerical evidence that operators
decouple from the spectrum as one approaches the 3d Ising point. We compare
this behavior to the analogous situation in 2d, where the disappearance of
operators can be understood in terms of degenerate Virasoro representations.Comment: 55 pages, many figures; v2 - refs and comments added, to appear in a
special issue of J.Stat.Phys. in memory of Kenneth Wilso
